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1.
  • 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
    • <p>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.</p>
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2.
  • 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
    • <p>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.</p>
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3.
  • 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. - 0264-9381 .- 1361-6382. ; 22:5, s. 791-802
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>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.</p>
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4.
  • Edgar, Brian, et al. (författare)
  • Petrov D vacuum spaces revisited identities and invariant classification
  • 2009
  • Ingår i: CLASSICAL AND QUANTUM GRAVITY. - 0264-9381. ; 26:10, s. 105022
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>For Petrov D vacuum spaces, two simple identities are rederived and some new identities are obtained, in a manageable form, by a systematic and transparent analysis using the GHP formalism. This gives a complete involutive set of tables for the four GHP derivatives on each of the four GHP spin coefficients and the one Weyl tensor component. It follows directly from these results that the theoretical upper bound on the order of covariant differentiation of the Riemann tensor required for a Karlhede classification of these spaces is reduced to two.</p>
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5.
  • Bäckdahl, Thomas, et al. (författare)
  • Calculation of, and bounds for, the multipole moments of stationary spacetimes
  • 2006
  • Ingår i: Classical and Quantum Gravity. - 0264-9381. ; 23:20, s. 5997-6006
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>In this paper, the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on <img src="http://ej.iop.org/images/0264-9381/23/20/019/cqg227478ieqn1.gif" />. We also give a bound on the multipole moments. This gives a proof of the 'necessary part' of a long-standing conjecture due to Geroch.</p>
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6.
  • Bäckdahl, Thomas, et al. (författare)
  • Explicit multipole moments of stationary axisymmetric spacetimes
  • 2005
  • Ingår i: Classical and Quantum Gravity. - 0264-9381 .- 1361-6382. ; 22:17, s. 3585-3594
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>In this paper, we study multipole moments of axisymmetric stationary asymptotically flat spacetimes. We show how the tensorial recursion of Geroch and Hansen can be reduced to a recursion of scalar functions. We also demonstrate how a careful choice of conformal factor collects all moments into one complex-valued function on <img src="http://ej.iop.org/images/0264-9381/22/17/017/cqg202281ieqn1.gif" />, where the moments appear as the derivatives at 0. As an application, we calculate the moments of the Kerr solution. We also discuss the freedom in choosing the potential for the moments.</p>
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7.
  • Abramowicz, Marek A, 1945-, et al. (författare)
  • Epicyclic oscillations of fluid bodies: II. Strong gravity
  • 2006
  • Ingår i: Classical and Quantum Gravity. - 0264-9381. ; 23:5, s. 1689-1696
  • Tidskriftsartikel (refereegranskat)abstract
    • Fluids in external gravity may oscillate with frequencies characteristic of the epicyclic motions of test particles. We explicitly demonstrate that global oscillations of a slender, perfect fluid torus around a Kerr black hole admit incompressible vertical and radial epicyclic modes. Our results may be directly relevant to one of the most puzzling astrophysical phenomena-high (hundreds of hertz) frequency quasiperiodic oscillations (QPOs) detected in x-ray fluxes from several black hole sources. Such QPOs are pairs of stable frequencies in the 3/2 ratio. It seems that they originate a few gravitational radii away from the black hole and thus their observations have the potential to become an accurate probe of super-strong gravity.
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8.
  • Alho, Artur, et al. (författare)
  • Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids
  • 2015
  • Ingår i: Classical and quantum gravity. - Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 32:14
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat Friedmann-Lemaitre-Robertson-Walker cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the ’attractor’ solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve the accuracy and range of the approximation by means of Pade approximants and compare with the slow-roll approximation. </p>
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9.
  • Ames, Ellery, et al. (författare)
  • On axisymmetric and stationary solutions of the self-gravitating Vlasov system
  • 2016
  • Ingår i: Classical and Quantum Gravity. - 0264-9381. ; 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.
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10.
  • Andersson, Fredrik, et al. (författare)
  • Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor
  • 2001
  • Ingår i: Classical and quantum gravity. - 0264-9381 .- 1361-6382. ; 18:12, s. 2297-2304
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2?(AA' LBCD)A', this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ?ABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD (= T(ABC)D) is given by LABCA' = ?A'DTABCD, while the second HABA'B' (= H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ? (AB' HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.</p>
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