| 1. |
- Andreasson, Håkan, 1966
(författare)
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Black Hole Formation from a Complete Regular Past for Collisionless Matter
- 2012
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Ingår i: Annales Henri Poincaré. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 13:7, s. 1511-1536
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Tidskriftsartikel (refereegranskat)abstract
- Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the Einstein-matter system with a "realistic" matter model. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass mIS= mIS (r) and the area radius r is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is in a sense analogous to the result (Christodoulou Commun Pure Appl Math 44:339-373, 1991) for a scalar field. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time .
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| 2. |
- Andreasson, Håkan, 1966
(författare)
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Existence of Steady States of the Massless Einstein-Vlasov System Surrounding a Schwarzschild Black Hole
- 2021
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 22, s. 4271-4297
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Tidskriftsartikel (refereegranskat)abstract
- We show that there exist steady states of the spherically symmetric massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole. To our knowledge this is the first result of static self-gravitating solutions to any massless Einstein-matter system which surround a black hole. We also include a numerical investigation about the properties of the shells.
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| 3. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Models for Self-Gravitating Photon Shells and Geons
- 2017
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 18:2, s. 681-705
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Tidskriftsartikel (refereegranskat)abstract
- We prove existence of spherically symmetric, static, self-gravitating photon shells as solutions to the massless Einstein-Vlasov system. The solutions are highly relativistic in the sense that the ratio 2m(r) / r is close to 8 / 9, where m(r) is the Hawking mass and r is the area radius. In 1955 Wheeler constructed, by numerical means, so-called idealized spherically symmetric geons, i.e., solutions of the Einstein-Maxwell equations for which the energy momentum tensor is spherically symmetric on a time average. The structure of these solutions is such that the electromagnetic field is confined to a thin shell for which the ratio 2m / r is close to 8 / 9, i.e., the solutions are highly relativistic photon shells. The solutions presented in this work provide an alternative model for photon shells or idealized spherically symmetric geons.
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| 4. |
- Andreasson, Håkan, 1966
(författare)
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Regularity Results for the Spherically Symmetric Einstein-Vlasov System
- 2010
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 11:5, s. 781-803
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Tidskriftsartikel (refereegranskat)abstract
- The spherically symmetric Einstein-Vlasov system is considered in Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose of the present work is to propose a method of approach for general initial data, which improves the regularity of the terms that need to be estimated compared to previous methods. We prove that global existence holds outside the center in both these coordinate systems. In the Schwarzschild case we improve the bound on the momentum support obtained in Rein et al. (Commun Math Phys 168:467-478, 1995) for compact initial data. The improvement implies that we can admit non-compact data with both ingoing and outgoing matter. This extends one of the results in Andreasson and Rein (Math Proc Camb Phil Soc 149:173-188, 2010). In particular our method avoids the difficult task of treating the pointwise matter terms. Furthermore, we show that singularities never form in Schwarzschild time for ingoing matter as long as 3m <= r. This removes an additional assumption made in Andreasson (Indiana Univ Math J 56:523-552, 2007). Our result in maximal-isotropic coordinates is analogous to the result in Rendall (Banach Center Publ 41:35-68, 1997), but our method is different and it improves the regularity of the terms that need to be estimated for proving global existence in general.
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| 5. |
- Banerjee, Sibasish, et al.
(författare)
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Exploring 5d BPS Spectra with Exponential Networks
- 2019
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Ingår i: Annales de l'Institute Henri Poincare. Physique theorique. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 20:12, s. 4055-4162
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Tidskriftsartikel (refereegranskat)abstract
- We develop geometric techniques for counting BPS states in five-dimensional gauge theories engineered by M theory on a toric Calabi–Yau threefold. The problem is approached by studying framed 3d–5d wall-crossing in the presence of a single M5 brane wrapping a special Lagrangian submanifold L. The spectrum of 3d–5d BPS states is encoded by the geometry of the manifold of vacua of the 3d–5d system, which further coincides with the mirror curve describing moduli of the Lagrangian brane. The information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for the exponential networks. For the simplest Calabi–Yau, C3 we reproduce the count of 5d BPS states and match predictions of 3d tt* geometry for the count of 3d–5d BPS states. We comment on applications of our construction to the study of enumerative invariants of toric Calabi–Yau threefolds.
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| 6. |
- Berger, Beverly K., et al.
(författare)
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Stability Within T2-Symmetric Expanding Spacetimes
- 2020
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Ingår i: Annales de l'Institute Henri Poincare. Physique theorique. - : Springer Nature. - 1424-0637 .- 1424-0661. ; 21:3, s. 675-703
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Tidskriftsartikel (refereegranskat)abstract
- We prove a nonpolarised analogue of the asymptotic characterisation of T-2-symmetric Einstein flow solutions completed recently by LeFloch and Smulevici. In this work, we impose a condition weaker than polarisation and so our result applies to a larger class. We obtain similar rates of decay for the normalised energy and associated quantities for this class. We describe numerical simulations which indicate that there is a locally attractive set for T-2-symmetric solutions not covered by our main theorem. This local attractor is distinct from the local attractor in our main theorem, thereby indicating that the polarised asymptotics are unstable.
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| 7. |
- Bjerklöv, Kristian
(författare)
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Positive lyapunov exponent and minimality for the continuous 1-d quasi-periodic Schrodinger equation with two basic frequencies
- 2007
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Ingår i: Annales de l'Institute Henri Poincare. Physique theorique. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 8:4, s. 687-730
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Tidskriftsartikel (refereegranskat)abstract
- We consider the time-independent quasi-periodic Schrodinger equation [GRAPHICS] with a potential function V : T-2 -> R of class C-2 with a unique non-degenerate global minimum, large coupling constants K-2 and energies E in the bottom of the spectrum of the associated Schrodinger operator. We obtain estimates on the Lyapunov exponents and the Lebesgue measure of the spectrum, as well as localization results. Moreover, we show that the projective flow on T-2 x P-1 induced by the Schrodinger equation often is minimal.
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| 8. |
- Bjerklöv, Kristian
(författare)
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The Dynamics of a Class of Quasi-Periodic Schrödinger Cocycles
- 2015
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Ingår i: Annales de l'Institute Henri Poincare. Physique theorique. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 16:4, s. 961-1031
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Tidskriftsartikel (refereegranskat)abstract
- Let f : T -> R be a Morse function of class C-2 with exactly two critical points, let omega is an element of T be Diopharitine, and let lambda > 0 be sufficiently large (depending on f and omega). For any value of the parameter E is an element of R, we make a careful analysis of the dynamics of the skew-product map Phi(E)(theta, r) = (theta + omega, lambda f(theta) - E - 1/r), acting on the "torus" T x (R) over cap. Here, (R) over cap denotes the projective space R boolean OR {infinity}. The map Phi(E) is intimately related to the quasi-periodic Schrodinger cocycle (omega, A(E)) : T x R-2 -> T x R-2, (theta, x) -> (theta + omega, A(E)(theta) . x), where A(E) : T -> SL(2, R) is given by A(E)(theta) = ((0)(-1) 1(lambda f(theta) - E)), E is an element of R. More precisely, (omega, A(E)) naturally acts on the space T x (R) over cap, and Phi(E) is the map thus obtained. The cocycle (omega, A(E)) arises when investigating the eigenvalue equation H(theta)u = Eu, where H-theta is the quasi-periodic Schrodinger operator (H(theta)u)(n) = -(u(n+1) + u(n-1)) + lambda f (theta + (n - 1)omega)u(n), (1) The (maximal) Lyapunov exponent of the Schrodinger cocycle (omega, A(E)) is greater than or similar to log lambda, uniformly in E is an element of R. This implies that the map PE has exactly two ergodic probability measures for all E is an element of R; (2) If E is on the edge of an open gap in the spectrum sigma(H), then there exist a phase 0 is an element of T and a vector u is an element of l(2)(Z), exponentially decaying at +/-infinity, such that H(theta)u = Eu;acting on the space l(2) (Z). It is well known that the spectrum of H-theta, sigma(H), is independent of the phase theta is an element of T. Under our assumptions on f, omega and lambda, Sinai (in J Stat Phys 46(5-6):861-909, 1987) has shown that sigma(H) is a Cantor set, and the operator H-theta has a pure-point spectrum, with exponentially decaying eig,enfunctions, for a.e. theta is an element of T The analysis of Phi(E) allows us to derive three main results: (3) The map Phi(E) is minimal iff E E is an element of sigma(H)\ {edges of open gaps}. In particular, Phi(E) is minimal for all E is an element of R for which the fibered rotation number alpha(E) associated with (omega, A(E)) is irrational with respect to omega.
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| 9. |
- Borisov, Denis, et al.
(författare)
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Spectrum of the Magnetic Schrödinger Operator in a Waveguide with Combined Boundary Conditions
- 2005
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Ingår i: Annales de l'Institute Henri Poincare. Physique theorique. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 6:2, s. 327-342
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Tidskriftsartikel (refereegranskat)abstract
- We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann(1). We deal with a smooth compactly supported field as well as with the Aharonov-Bohm field. We give an estimate on the maximal length of the window, for which the discrete spectrum of the considered operator will be empty. In the case of a compactly supported field we also give a sufficient condition for the presence of eigenvalues below the essential spectrum.
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| 10. |
- Bounemoura, Abed, et al.
(författare)
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Positive Measure of Effective Quasi-Periodic Motion Near a Diophantine Torus
- 2023
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Ingår i: Annales de l'Institute Henri Poincare. Physique theorique. - : Springer Nature. - 1424-0637 .- 1424-0661. ; 24:9, s. 3289-3304
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Tidskriftsartikel (refereegranskat)abstract
- It was conjectured by Herman that an analytic Lagrangian Diophantine quasi-periodic torus T, invariant by a real-analytic Hamiltonian system, is always accumulated by a set of positive Lebesgue measure of other Lagrangian Diophantine quasi-periodic invariant tori. While the conjecture is still open, we will prove the following weaker statement: there exists an open set of positive measure (in fact, the relative measure of the complement is exponentially small) around T such that the motion of all initial conditions in this set is “effectively” quasi-periodic in the sense that they are close to being quasi-periodic for an interval of time, which is doubly exponentially long with respect to the inverse of the distance to T. This open set can be thought of as a neighborhood of a hypothetical invariant set of Lagrangian Diophantine quasi-periodic tori, which may or may not exist.
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