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1.	Barack, Leor, et al. (författare) Black holes, gravitational waves and fundamental physics : a roadmap 2019 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 36:14 Forskningsöversikt (refereegranskat)abstract The grand challenges of contemporary fundamental physics dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.
2.	Günther, Sebastian, et al. (författare) A numerical stability analysis for the Einstein-Vlasov system 2021 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:3 Tidskriftsartikel (refereegranskat)abstract We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the conjecture that the first binding energy maximum along a one-parameter family of steady states signals the onset of instability. Beyond this maximum perturbed solutions either collapse to a black hole, form heteroclinic orbits, or eventually fully disperse. Contrary to earlier research, we find that a negative binding energy does not necessarily correspond to fully dispersing solutions. We also comment on the so-called turning point principle from the viewpoint of our numerical results. The physical reliability of the latter is strengthened by obtaining consistent results in the three different coordinate systems and by the systematic use of dynamically accessible perturbations.
3.	Bradley, Michael, et al. (författare) Density growth in Kantowski-Sachs cosmologies with cosmological constant 2012 Ingår i: Classical and quantum gravity. - Bristol : Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 29:9, s. 095023- Tidskriftsartikel (refereegranskat)abstract In this work the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analyzed both analytically andnumerically. In particular the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered.We find that typically the density gradient in the bouncing direction experiences a local maximum at or slightly after the bounce.
4.	Aasi, J., et al. (författare) The characterization of Virgo data and its impact on gravitational-wave searches 2012 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 1361-6382 .- 0264-9381. ; 29:15 Tidskriftsartikel (refereegranskat)abstract Between 2007 and 2010 Virgo collected data in coincidence with the LIGO and GEO gravitational-wave (GW) detectors. These data have been searched for GWs emitted by cataclysmic phenomena in the universe, by non-axisymmetric rotating neutron stars or from a stochastic background in the frequency band of the detectors. The sensitivity of GW searches is limited by noise produced by the detector or its environment. It is therefore crucial to characterize the various noise sources in a GW detector. This paper reviews the Virgo detector noise sources, noise propagation, and conversion mechanisms which were identified in the three first Virgo observing runs. In many cases, these investigations allowed us to mitigate noise sources in the detector, or to selectively flag noise events and discard them from the data. We present examples from the joint LIGO-GEO-Virgo GW searches to show how well noise transients and narrow spectral lines have been identified and excluded from the Virgo data. We also discuss how detector characterization can improve the astrophysical reach of GW searches.
5.	Ames, Ellery, 1984, et al. (författare) On axisymmetric and stationary solutions of the self-gravitating Vlasov system 2016 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 33:15 Tidskriftsartikel (refereegranskat)abstract Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
6.	Andersson, Lars Erik, et al. (författare) Decay of solutions to the Maxwell equation on the Schwarzschild background 2016 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 33:8 Tidskriftsartikel (refereegranskat)abstract A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor H-ab defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current H-ab (partial derivative(t))(b). The tensor Hab vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.
7.	Andreasson, Håkan, 1966, et al. (författare) A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric EinsteinVlasov system 2006 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23, s. 3659-3677 Tidskriftsartikel (refereegranskat)abstract The stability features of steady states of the spherically symmetric EinsteinVlasov system are investigated numerically. We find support for the conjecture by Zel'dovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.
8.	Andreasson, Håkan, 1966, et al. (författare) A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system 2009 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:14 Tidskriftsartikel (refereegranskat)abstract We construct, by numerical means, static solutions of the spherically symmetric Einstein-Vlasov-Maxwell system and investigate various features of the solutions. This extends a previous investigation (Andreasson and Rein 2007 Class. Quantum Grav. 24 1809) of the chargeless case. We study the possible shapes of the energy density profile as a function of the area radius when the electric charge of an individual particle is varied as a parameter. We find profiles which are multi-peaked, where the peaks are separated either by vacuum or a thin atmosphere, and we find that for a sufficiently large charge parameter the solutions break down at a finite radius. Furthermore, we investigate the inequality root M <= root R/3 + root R/9 + Q(2)/3R, which is derived in Andreasson (2009 Commun. Math. Phys. 288 715) for general matter models, and we find that it is sharp for the Einstein-Vlasov-Maxwell system. Here M is the ADM mass, Q is the charge and R is the area radius of the boundary of the static object. We find two classes of solutions with this property, while there is only one in the chargeless case. In particular we find numerical evidence for the existence of arbitrarily thin shell solutions to the Einstein-Vlasov-Maxwell system. Finally, we consider one-parameter families of steady states, and we find spirals in the mass-radius diagram for all examples of the microscopic equation of state which we consider.
9.	Andreasson, Håkan, 1966, et al. (författare) Bounds on M/R for charged objects with positive cosmological constant 2012 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 29:9 Tidskriftsartikel (refereegranskat)abstract We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant Lambda. If r denotes the area radius, m(g) and q the gravitational mass and charge of a sphere with area radius r respectively, we find that for any solution which satisfies the condition p + 2p(perpendicular to) +/- <= rho, where p >= 0 and p(perpendicular to) are the radial and tangential pressures respectively, rho >= 0 is the energy density, and for which 0 <= q(2)/r(2) + Lambda r(2) <= 1, the inequality m(g)/r <= 2/9 + q(2)/3r(2)-Lambda r(2)/3 + 2/9 root 1 + 3q(2)/r(2) + 3 Lambda r(2) holds. We also investigate the issue of sharpness, and we showthat the inequality is sharp in a few cases but generally this question is open.
10.	Andreasson, Håkan, 1966, et al. (författare) Spherically symmetric steady states of John elastic bodies in general relativity 2014 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 31:16 Tidskriftsartikel (refereegranskat)abstract We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large (z approximate to 2.8) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.
11.	Bao, Ling, 1980, et al. (författare) Aspects of higher curvature terms and U-duality 2007 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 25:9 Tidskriftsartikel (refereegranskat)abstract We discuss various aspects of dimensional reduction of gravity with theEinstein-Hilbert action supplemented by a lowest order deformation formed asthe Riemann tensor raised to powers two, three or four. In the case of R^2 wegive an explicit expression, and discuss the possibility of extended cosetsymmetries, especially SL(n+1,Z) for reduction on an n-torus to threedimensions. Then we start an investigation of the dimensional reduction of R^3and R^4 by calculating some terms relevant for the coset formulation, aiming inparticular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and aninvestigation of the derivative structure. We emphasise some issues concerningthe need for the introduction of non-scalar automorphic forms in order torealise certain expected enhanced symmetries.
12.	Bundzik, Daniel, et al. (författare) The geometry of fractional D1-branes 2004 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 1361-6382 .- 0264-9381. ; 21:16, s. 3985-3993 Tidskriftsartikel (refereegranskat)abstract We find explicit solutions of type IIB string theory on R-4/Z(2) corresponding to the classical geometry of fractional D1-branes. From the supergravity solution obtained, we capture perturbative information about the running of the coupling constant and the metric on the moduli space of N = 4, D = 2 super Yang-Mills.
13.	Gran, Ulf, 1973, et al. (författare) IIB horizons 2013 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 30:20 Tidskriftsartikel (refereegranskat)abstract We solve the Killing spinor equations for all near-horizon IIB geometries which preserve at least one supersymmetry. We show that generic horizon sections are eight-dimensional almost Hermitian spin(c) manifolds. Special cases include horizon sections with a Spin(7) structure and those for which the Killing spinor is pure. We also explain how the common sector horizons and the horizons with only 5-form flux are included in our general analysis. We investigate several special cases mainly focusing on the horizons with constant scalars admitting a pure Killing spinor and find that some of these exhibit a generalization of the 2-SCYT condition that arises in the horizons with 5-form fluxes only. We use this to construct new examples of near-horizon geometries with both 3-form and 5-form fluxes.
14.	Gran, Ulf, 1973, et al. (författare) Invariant Killing spinors in 11D and type II supergravities 2009 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:15 Tidskriftsartikel (refereegranskat)abstract We present all isotropy groups and associated $\Sigma$ groups, up to discrete identifications of the component connected to the identity, of spinors of eleven-dimensional and type II supergravities. The $\Sigma$ groups are products of a Spin group and an R-symmetry group of a suitable lower dimensional supergravity theory. Using the case of SU(4)-invariant spinors as a paradigm, we demonstrate that the $\Sigma$ groups, and so the R-symmetry groups of lower-dimensional supergravity theories arising from compactifications, have disconnected components. These lead to discrete symmetry groups reminiscent of R-parity. We examine the role of disconnected components of the $\Sigma$ groups in the choice of Killing spinor representatives and in the context of compactifications.
15.	Jonsson, Rickard, 1973 (författare) A covariant formalism of spin precession with respect to a reference congruence 2006 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 37-59 Tidskriftsartikel (refereegranskat)abstract We derive an effectively three-dimensional relativistic spin precession formalism. The formalism is applicable to any spacetime where an arbitrary timelike reference congruence of worldlines is specified. We employ what we call a stopped spin vector which is the spin vectorthat we would get if we momentarily make a pure boost of the spin vector to stop it relative to the congruence. Starting from the Fermi transport equation for the standard spin vector we derive a corresponding transport equation for the stopped spin vector. Employing a spacetime transport equation for a vector along a worldline, corresponding to spatial parallel transport with respect to the congruence, we can write down a precession formula for a gyroscope relative to the local spatial geometry defined by the congruence. This general approach has already been pursued by Jantzen et al (see e.g. Jantzen R T, Carini P and Bini D 1992 Ann. Phys. 215 1-50), but the algebraic form of our respective expressions differs. We are also applying the formalism to a novel type of spatial parallel transport introduced in Jonsson (2006 Class. Quantum Grav. 23 1), as well as verifying the validity of the intuitive approach of aforthcoming paper (Jonsson 2006 forthcoming) where gyroscope precession is explained entirely as a double Thomas type of effect. We also present the resulting formalism in explicit three-dimensional form (using the boldface vector notation), and give examples of applications.
16.	Jonsson, Rickard, 1973, et al. (författare) Generalizing optical geometry 2006 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 61-76 Tidskriftsartikel (refereegranskat)abstract We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.
17.	Jonsson, Rickard, 1973 (författare) Inertial forces and the foundations of optical geometry 2006 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 1-36 Tidskriftsartikel (refereegranskat)abstract Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in general relativity. Inspired by the works of Abramowicz et al (see e.g. Abramowicz and Lasota 1997 Class. Quantum Grav. 14 A23-30), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory have been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference congruence is shearing), appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon always follows a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61). For the particular case when the shear tensor vanishes, we present the inertial force equation in a three-dimensional form (using the bold-face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen and co-workers (see e.g. Bini et al 1997 Int. J. Mod. Phys. D 6 143-98).
18.	Jonsson, Rickard, 1973 (författare) Optical geometry across the horizon 2006 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 77-89 Tidskriftsartikel (refereegranskat)abstract In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework.
19.	LIGO, Scientific Collaboration, et al. (författare) Predictions for the rates of compact binary coalescences observable by ground-based gravitational-wave detectors 2010 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 1361-6382 .- 0264-9381. ; 27:17 Tidskriftsartikel (refereegranskat)abstract We present an up-to-date, comprehensive summary of the rates for all types of compact binary coalescence sources detectable by the initial and advanced versions of the ground-based gravitational-wave detectors LIGO and Virgo. Astrophysical estimates for compact-binary coalescence rates depend on a number of assumptions and unknown model parameters and are still uncertain. Themost confident among these estimates are the rate predictions for coalescing binary neutron stars which are based on extrapolations from observed binary pulsars in our galaxy. These yield a likely coalescence rate of 100 Myr(-1) per Milky Way Equivalent Galaxy (MWEG), although the rate could plausibly range from 1 Myr(-1) MWEG(-1) to 1000 Myr(-1) MWEG(-1) (Kalogera et al 2004 Astrophys. J. 601 L179; Kalogera et al 2004 Astrophys. J. 614 L137 ( erratum)). We convert coalescence rates into detection rates based on data from the LIGO S5 and Virgo VSR2 science runs and projected sensitivities for our advanced detectors. Using the detector sensitivities derived from these data, we find a likely detection rate of 0.02 per year for Initial LIGO-Virgo interferometers, with a plausible range between 2 x 10(-4) and 0.2 per year. The likely binary neutron-star detection rate for the Advanced LIGO-Virgo network increases to 40 events per year, with a range between 0.4 and 400 per year.
20.	Nilsson, Bengt E W, 1952 (författare) Light-cone analysis of ungauged and topologically gauged BLG theories 2009 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:17 Tidskriftsartikel (refereegranskat)abstract We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in Gran and Nilsson (2009 J. High Energy Phys. JHEP03(2009) 074 (arXiv:0809.4478 [hep-th]))) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG light-cone theory looks more conventional and, apart from the order of the interaction terms, resembles N = 4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given at the quadratic order together with a suggested form for the quartic terms. Some problems with constructing the sixth-order interaction terms are also discussed. In the topologically gauged case, we analyze the field equations related to the three Chern-Simons-type terms of N = 8 conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.
21.	Nilsson, Bengt E W, 1952, et al. (författare) Superconformal M2-branes and generalized Jordan triple systems 2009 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:7, s. Article Number: 075007 - Tidskriftsartikel (refereegranskat)abstract Three-dimensional conformal theories with six supersymmetries and SU(4) R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the four-index structure constants in an appropriate form, the Chern-Simons part of the action immediately suggests a connection to such triple systems. In contrast to the previously considered 3-algebras, the additional structure of a generalized Jordan triple system is associated with a graded Lie algebra, which corresponds to an extension of the gauge group. In this paper we show that the whole theory with six manifest supersymmetries can be naturally expressed in terms of such a graded Lie algebra. Also the Bagger, Lambert and Gustavsson theory with eight supersymmetries is included as a special case.
22.	Edgar, Brian, 1945-, et al. (författare) A local potential for the Weyl tensor in all dimensions 2004 Ingår i: Classical and quantum gravity. - 0264-9381 .- 1361-6382. ; 21:22 Tidskriftsartikel (refereegranskat)abstract In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential - a double (2, 3)-form, Pabcde - for the Weyl curvature tensor Cabcd, and more generally for all tensors Wabcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor - a double (2, 1)-form, Habc - is proven to be a particular case of the new potential: its double dual.
23.	Edgar, Brian, 1945-, et al. (författare) Obtaining a class of type N pure radiation metrics using invariant operators 2005 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 22:5, s. 791-802 Tidskriftsartikel (refereegranskat)abstract We develop further the integration procedure in the generalized invariant formalism, and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A major addition to the technique is the introduction of non-intrinsic elements in the generalized invariant formalism, which can be exploited to keep calculations manageable.
24.	Khoo, Fech Scen, et al. (författare) Lux in obscuro : photon orbits of extremal black holes revisited 2016 Ingår i: Classical and quantum gravity. - : Institute of Physics Publishing. - 0264-9381 .- 1361-6382. ; 33:23 Tidskriftsartikel (refereegranskat)abstract It has been shown in the literature that the event horizon of an asymptotically flat extremal Reissner-Nordstrom black hole is also a stable photon sphere. We further clarify this statement and give a general proof that this holds for a large class of static spherically symmetric black hole spacetimes with an extremal horizon. In contrast, in the Doran frame, an asymptotically flat extremal Kerr black hole has an unstable photon orbit on the equatorial plane of its horizon. In addition, we show that an asymptotically flat extremal Kerr-Newman black hole exhibits two equatorial photon orbits if a < M/2, one of which is on the extremal horizon in the Doran frame and is stable, whereas the second one outside the horizon is unstable. For a > M/2, there is only one equatorial photon orbit, located on the extremal horizon, and it is unstable. There can be no photon orbit on the horizon of a non-extremal Kerr-Newman black hole.
25.	Alho, Artur, et al. (författare) Cosmological global dynamical systems analysis 2022 Ingår i: Classical and quantum gravity. - : Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 39:14, s. 1-14 Tidskriftsartikel (refereegranskat)abstract We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear hyperbolic fixed point analysis, we do a center manifold analysis of the non-hyperbolic fixed points associated with bifurcations. More importantly though, we construct monotonic functions and a Dulac function. Together with the complete local fixed point analysis this leads to proofs that describe the entire global dynamics of these models, thereby complementing previous local results in the literature.
26.	Alho, Artur, et al. (författare) Dynamical systems in perturbative scalar field cosmology 2020 Ingår i: Classical and quantum gravity. - : American Institute of Physics (AIP). - 0264-9381 .- 1361-6382. ; 37:22 Tidskriftsartikel (refereegranskat)abstract We derive a newregulardynamical system on a three-dimensionalcompactstate space describing linear scalar perturbations of spatially flat Robertson-Walker geometries for relativistic models with a minimally coupled scalar field with an exponential potential. This enables us to construct the global solution space, illustrated with figures, where known solutions are shown to reside on special invariant sets. We also use our dynamical systems approach to obtain new results about the comoving and uniform density curvature perturbations. Finally we show how to extend our approach to more general scalar field potentials. This leads to state spaces where the state space of the models with an exponential potential appears as invariant boundary sets, thereby illustrating their role as building blocks in a hierarchy of increasingly complex cosmological models.
27.	Ames, E., et al. (författare) Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system 2021 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:10 Tidskriftsartikel (refereegranskat)abstract We numerically investigate the dynamics near black hole formation of solutions to the Einstein-Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the (2 + 1) + 1 formulation of the Einstein field equations in axisymmetry. Solutions are launched from non-stationary initial data and exhibit type I critical behaviour. In particular, we find lifetime scaling in solutions containing black holes, and support that the critical solutions are stationary. Our results contain examples of solutions that form black holes, perform damped oscillations, and appear to disperse. We prove that complete dispersal of the solution implies that it has nonpositive binding energy.
28.	Ames, Ellery, 1984, et al. (författare) Stationary solutions of the axially symmetric Einstein-Vlasov system: present status and open problems 2024 Ingår i: Classical and Quantum Gravity. - 0264-9381 .- 1361-6382. ; 41:7 Forskningsöversikt (refereegranskat)abstract The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in Ames et al (2016 Class. Quantum Grav. 33 155008; 2019 Phys. Rev. D 99 024012) is open source, see Ames and Logg (2023 J. Open Source Softw. 8 5979). In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.
29.	Apolo, Luis, et al. (författare) Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity 2017 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 34:10 Tidskriftsartikel (refereegranskat)abstract We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders. This theory is based on the SO(1, 5) group, in analogy with the SO(2, 4) formulation of conformal gravity, but has a quadratic spectrum free of ghost instabilities. The action contains a vector field associated with a local SO(2) symmetry which is manifest in the vielbein formulation of the theory. We show that, in a perturbative expansion, the SO(2) symmetry transmutes into the PM transformations of a massive spin-2 field. In this context, the vector field is crucial to circumvent earlier obstructions to an order-by-order construction of PM symmetry. Although the non-linear theory lacks enough first class constraints to remove all helicity-0 modes from the spectrum, the PM transformations survive to all orders. The absence of ghosts and strong coupling effects at the non-linear level are not addressed here.
30.	Bengtsson, Ingemar, et al. (författare) Black hole lattices under the microscope 2018 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 35:14 Tidskriftsartikel (refereegranskat)abstract It is known how to choose initial data for Einstein's equations describing an arbitrary number of black holes at a moment of time symmetry. This idea has been used to give insight into the cosmological averaging problem. We study the local curvature of the initial data space, for configurations of 8, 120, or 600 black holes obtained by choosing points either regularly or randomly on a 3-sphere. We conclude that the asymptotic regions are remarkably close to that of Schwarzschild, while the region in between shows interesting behaviour. The cosmological back reaction as defined in the recent literature is actually a bit smaller for the random configurations.
31.	Bentivegna, Eloisa, et al. (författare) Black-hole lattices as cosmological models 2018 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 35:17 Tidskriftsartikel (refereegranskat)abstract The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a specific subclass of discrete cosmologies, black-hole lattice models. In particular, we illustrate the techniques used for the construction of these spacetimes, and examine their resulting physical properties. This includes their large-scale dynamics, the dressing of mass due to the interaction between individual black holes, along with features of direct observational interest such as the distance-to-redshift relation. This collection of results provides a novel perspective on the physical effects of averaging in general relativity, as well as on the emergence of gravitational structures from solutions with isolated objects.
32.	Bergshoeff, E. A., et al. (författare) Generalized Newton-Cartan geometries for particles and strings 2023 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 40:7 Tidskriftsartikel (refereegranskat)abstract We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure group, we describe torsionful geometries with independent torsion tensors. A characteristic feature of the non-Lorentzian geometries we consider is that some of the torsion tensors are so-called 'intrinsic torsion' tensors. Setting some components of these intrinsic torsion tensors to zero leads to constraints on the geometry. For both particles and strings, we discuss various such constraints that can be imposed consistently with the structure group symmetries. In this way, we reproduce several results in the literature.
33.	Brandenburg, Axel, et al. (författare) The scalar, vector, and tensor modes in gravitational wave turbulence simulations 2021 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:14 Tidskriftsartikel (refereegranskat)abstract We study the gravitational wave (GW) signal sourced by primordial turbulence that is assumed to be present at cosmological phase transitions like the electroweak and quantum chromodynamics phase transitions. We consider various models of primordial turbulence, such as those with and without helicity, purely hydrodynamical turbulence induced by fluid motions, and magnetohydrodynamic turbulence whose energy can be dominated either by kinetic or magnetic energy, depending on the nature of the turbulence. We also study circularly polarized GWs generated by parity violating sources such as helical turbulence. Our ultimate goal is to determine the efficiency of GW production through different classes of turbulence. We find that the GW energy and strain tend to be large for acoustic or irrotational turbulence, even though its tensor mode amplitude is relatively small at most wave numbers. Only at very small wave numbers is the spectral tensor mode significant, which might explain the efficient GW production in that case.
34.	Cabrera Pacheco, A. J., et al. (författare) Asymptotically flat extensions of CMC Bartnik data 2017 Ingår i: Classical and quantum gravity. - : Institute of Physics Publishing. - 0264-9381 .- 1361-6382. ; 34:10 Tidskriftsartikel (refereegranskat)abstract Let g be a metric on the 2-sphere with positive Gaussian curvature and H be a positive constant. Under suitable conditions on (g, H), we construct smooth, asymptotically flat 3-manifolds M with non-negative scalar curvature, with outer-minimizing boundary isometric to and having mean curvature H, such that near infinity M is isometric to a spatial Schwarzschild manifold whose mass m can be made arbitrarily close to a constant multiple of the Hawking mass of . Moreover, this constant multiplicative factor depends only on (g, H) and tends to 1 as H tends to 0. The result provides a new upper bound of the Bartnik mass associated with such boundary data.
35.	Casalino, Alessandro, et al. (författare) Alive and well : mimetic gravity and a higher-order extension in light of GW170817 2019 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 36:1 Tidskriftsartikel (refereegranskat)abstract The near-simultaneous multi-messenger detection of the gravitational wave (GW) event GW170817 and its optical counterpart, the short gamma-ray burst GRB170817A, implies that deviations of the GW speed from the speed of light are restricted to being of Omicron(10(-15)). In this note, we study the implications of this bound for mimetic gravity and confirm that in the original setting of the theory, GWs propagate at the speed of light, hence ensuring agreement with the recent multi-messenger detection. A higher-order extension of the original mimetic theory, appearing in the low-energy limit of projectable Horava-Lifshitz gravity, is then considered. Performing a Bayesian statistical analysis where we compare the predictions of the higher-order mimetic model for the speed of GWs against the observational bound from GW170817/GRB170817A, we derive constraints on the three free parameters of the theory. Imposing the absence of both ghost instabilities and superluminal propagation of scalar and tensor perturbations, we find very stringent 95% confidence level upper limits of similar to 7 x 10(-15) and similar to 4 x 10(-15)on the coupling strengths of Lagrangian terms of the form del(mu)del(nu)phi del(mu)del(nu)phi and (square phi)(2) respectively, with phi the mimetic field. We discuss implications of the obtained bounds for mimetic theories. This work presents the first ever robust comparison of a mimetic theory to observational data.
36.	Golovnev, Alexey, et al. (författare) On the covariance of teleparallel gravity theories 2017 Ingår i: Classical and quantum gravity. - : Institute of Physics Publishing (IOPP). - 0264-9381 .- 1361-6382. ; 34:14 Tidskriftsartikel (refereegranskat)abstract The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of the Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models are discussed. A by-product is a new form of f (T) field equations.
37.	Gonzalez, Alejandra, et al. (författare) Second release of the CoRe database of binary neutron star merger waveforms 2023 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 40:8 Tidskriftsartikel (refereegranskat)abstract We present the second data release of gravitational waveforms from binary neutron star (BNS) merger simulations performed by the Computational Relativity (CoRE) collaboration. The current database consists of 254 different BNS configurations and a total of 590 individual numerical-relativity simulations using various grid resolutions. The released waveform data contain the strain and the Weyl curvature multipoles up to l = m = 4. They span a significant portion of the mass, mass-ratio, spin and eccentricity parameter space and include targeted configurations to the events GW170817 and GW190425. CoRE simulations are performed with 18 different equations of state, seven of which are finite temperature models, and three of which account for nonhadronic degrees of freedom. About half of the released data are computed with high-order hydrodynamics schemes for tens of orbits to merger; the other half is computed with advanced microphysics. We showcase a standard waveform error analysis and discuss the accuracy of the database in terms of faithfulness. We present ready-to-use fitting formulas for equation of state-insensitive relations at merger (e.g. merger frequency), luminosity peak, and post-merger spectrum.
38.	Gran, Ulf, 1973, et al. (författare) All superalgebras for warped AdS2 and black hole near horizon geometries 2019 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 36:23 Tidskriftsartikel (refereegranskat)abstract We identify all symmetry superalgebras ? of near horizon geometries of black holes with a Killing horizon, assuming the solution is smooth and that the spatial cross section of the event horizon is compact without boundary. This includes all warped AdS2 backgrounds with the most general allowed fluxes in 10- and 11-dimensional supergravities. If the index of a particular Dirac operator vanishes, we find that the even symmetry subalgebra decomposes as ?0=??(2,ℝ)⊕?0, where ?0/? is the Lie algebra of a group that acts transitively and effectively on spheres, and ? is the center of ?. If the Dirac operator index does not vanish, then the symmetry superalgebra is nilpotent with one even generator. We also demonstrate that there are no near horizon geometries, and also therefore no warped AdS2 backgrounds, in 10- and 11-dimensions that preserve more than 16 supersymmetries.
39.	Gran, Ulf, 1973, et al. (författare) On supersymmetric anti-de Sitter, de Sitter and Minkowski flux backgrounds 2018 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 35:6 Tidskriftsartikel (refereegranskat)abstract We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter spaces. We find that there are supersymmetric de Sitter solutions in supergravity theories including maximally supersymmetric ones in 10- and 11-dimensional supergravities. Moreover, warped flux Minkowski backgrounds can admit Killing spinors which are not Killing on the Minkowski subspace and therefore cannot be put in a factorized form.
40.	Hossenfelder, Sabine, et al. (författare) Analogue gravity models from conformal rescaling 2017 Ingår i: Classical and quantum gravity. - : IOP PUBLISHING LTD. - 0264-9381 .- 1361-6382. ; 34:16 Tidskriftsartikel (refereegranskat)abstract Analogue gravity is based on a mathematical identity between quantum field theory in curved space-time and the propagation of perturbations in certain condensed matter systems. But not every curved space-time can be simulated in such a way. For analogue gravity to work, one needs not only a condensed matter system that generates the desired metric tensor, but this system then also has to obey its own equations of motion. However, the relation to the metric tensor usually overdetermines the equations of the underlying condensed matter system, such that they in general cannot be fulfilled. In this case the desired metric does not have an analogue. Here, we show that the class of metrics that have an analogue is larger than previously thought. The reason is that the analogue metric is only defined up to a choice of parametrization of the perturbation in the underlying condensed matter system. In this way, the class of analogue gravity models can be vastly expanded.
41.	Hutschenreuter, Sebastian, et al. (författare) The primordial magnetic field in our cosmic backyard 2018 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 35:15 Tidskriftsartikel (refereegranskat)abstract We reconstruct for the first time the three dimensional structure of magnetic fields on cosmological scales, which were seeded by density perturbations during the radiation dominated epoch of the Universe and later on were evolved by structure formation. To achieve this goal, we rely on three dimensional initial density fields inferred from the 2M++ galaxy compilation via the Bayesian BORG algorithm. Using those, we estimate the magnetogenesis by the so called Harrison mechanism. This effect produced magnetic fields exploiting the different photon drag on electrons and ions in vortical motions, which are exited due to second order perturbation effects in the Early Universe. Subsequently we study the evolution of these seed fields through the non- linear cosmic structure formation by virtue of a magneto-hydrodynamics simulation to obtain a 3D estimate for the structure of this primordial magnetic field component today. At recombination we obtain large scale magnetic field strengths around 10(-23) G, with a power spectrum peaking at about 2 Mpc(-1) h in comoving scales. At present we expect this evolved primordial field to have strengths above approximate to 10(-27) G and approximate to 10(-29) G in clusters of galaxies and voids, respectively. We also calculate the corresponding Faraday rotation measure map and show the magnetic field morphology and strength for specific objects of the Local Universe. These results provide a reliable lower limit on the primordial component of the magnetic fields in these structures.
42.	Högås, Marcus, et al. (författare) Generalized Vaidya solutions in bimetric gravity 2020 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 37:14 Tidskriftsartikel (refereegranskat)abstract In general relativity, the endpoint of spherically symmetric gravitational collapse is a Schwarzschild-[(A)dS] black hole. In bimetric gravity, it has been speculated that a static end state must also be Schwarzschild-[(A)dS]. To this end, we present a set of exact solutions, including collapsing massless dust particles. For these, the speculation is confirmed.
43.	Jacobsson, S., et al. (författare) Second order symmetry operators for the massive Dirac equation 2023 Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 40:4 Tidskriftsartikel (refereegranskat)abstract Employing the covariant language of two-spinors, we find what conditions a curved four-dimensional Lorentzian spacetime must satisfy for existence of a second order symmetry operator for the massive Dirac equation. The conditions are formulated as existence of a set of Killing spinors satisfying a set of covariant linear differential equations. Using these Killing spinors, we then state the most general form of such an operator. Partial results for the zeroth and first order are presented and interpreted as well. Computer algebra tools from the Mathematica package suite xAct were used for the calculations.
44.	Kinney, William H., et al. (författare) The zoo plot meets the swampland : mutual (in)consistency of single-field inflation, string conjectures, and cosmological data 2019 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 36:11 Tidskriftsartikel (refereegranskat)abstract We consider single-field inflation in light of string-motivated 'swampland' conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion Delta(phi) less than or similar to M-Pl, in combination with a sufficiently steep potential, MPlV phi/V greater than or similar to O(1). Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the n(S)-r 'zoo plot' of inflationary models, and find that consistency with the Planck satellite and BICEP2/Keck Array requires MPlV phi/V less than or similar to 0.1 and -0.02 less than or similar to M-Pl(2)/V-phi phi < 0, in strong tension with swampland conjectures. Extension to non-canonical models such as DBI Inflation does not significantly weaken the bound.
45.	Kocic, Mikica (författare) Geometric mean of bimetric spacetimes 2021 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:7 Tidskriftsartikel (refereegranskat)abstract We use the geometric mean to parametrize metrics in the Hassan-Rosen ghost-free bimetric theory and pose the initial-value problem. The geometric mean of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended to quadratic forms having the Lorentzian signature, say metrics g and f. In such a case, the null cone of the geometric mean metric h is in the middle of the null cones of g and f appearing as a geometric average of a bimetric spacetime. The parametrization based on h ensures the reality of the square root in the ghost-free bimetric interaction potential. Subsequently, we derive the standard n + 1 decomposition in a frame adapted to the geometric mean and state the initial-value problem, that is, the evolution equations, the constraints, and the preservation of the constraints equation.
46.	Kocic, Mikica, et al. (författare) Initial data and first evolutions of dust clouds in bimetric relativity 2020 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 37:16 Tidskriftsartikel (refereegranskat)abstract We present a method for solving the constraint equations in the Hassan-Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called Lane-Emden-like equations. Using a numerical code which solves the evolution equations in the standard 3 + 1 form, we also obtain a short-term development of the initial data for these bimetric spherical clouds. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen-Birkhoff theorem in bimetric relativity.
47.	Kocic, Mikica, et al. (författare) On the ratio of lapses in bimetric relativity 2019 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 36:22 Tidskriftsartikel (refereegranskat)abstract The two lapse functions in the Hassan–Rosen bimetric theory are not independent. Without knowing the relation between them, one cannot evolve the equations in the 3+1 formalism. This work computes the ratio of lapses for the spherically symmetric case, which is a prerequisite for numerical bimetric relativity.
48.	Lindström, Ulf, et al. (författare) Gravitational duality, Palatini variation and boundary terms : a synopsis 2023 Ingår i: Classical and quantum gravity. - : Institute of Physics Publishing (IOPP). - 0264-9381 .- 1361-6382. ; 40:8 Tidskriftsartikel (refereegranskat)abstract We consider f(R) gravity and Born–Infeld–Einstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the archetypical treatment being that of Eddington–Schrödinger (ES) duality between cosmological Einstein and Eddington theories. For dimensions , we find that this requires f(R) to have a specific form which makes the model Weyl invariant, and that its Eddington reduction is then equivalent to that of BIE with certain parameters. For D = 2 dimensions, where ES duality is not applicable, we find that both models are Weyl invariant and equivalent to a first order formulation of the bosonic string. We also discuss the form of the boundary terms needed for the variational principle to be well defined on manifolds with non-null boundaries. This requires a modification of the Gibbons–Hawking–York (GHY) boundary term for gravity. This modification also means that the dualities between metric and connection formulations are consistent and include the boundary terms.
49.	Lindström, Ulf, et al. (författare) New currents with Killing-Yano tensors 2021 Ingår i: Classical and quantum gravity. - : Institute of Physics Publishing (IOPP). - 0264-9381 .- 1361-6382. ; 38:19 Tidskriftsartikel (refereegranskat)abstract New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing-Yano tensors (KYTs) are described. These relations are then used to introduce novel conserved 'currents' involving such KYTs. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for matter coupled to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on. In particular we show that it vanishes for rank (D - 1) KYTs in D dimensions.
50.	Lueben, Marvin, et al. (författare) Bimetric cosmology is compatible with local tests of gravity 2020 Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 37:4 Tidskriftsartikel (refereegranskat)abstract Recently, Kenna-Allison et al claimed that bimetric gravity cannot give rise to a viable cosmological expansion history while at the same time being compatible with local gravity tests. In this note we review that claim and combine various results from the literature to provide several simple counter examples. We conclude that the results of Kenna-Allison et al cannot hold in general.

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