Strong Cosmic Censorship for Surface‐Symmetric Cosmological Spacetimes with Collisionless Matter

Dafermos, Mihalis; Rendall, Alan D.

doi:10.1002/cpa.21628

Cited by 26 publications

(43 citation statements)

References 62 publications

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“…In order to control V 2 V 1 f (x, p) it is therefore necessary to estimate the J 2 derivatives of the components of J 1 along s → exp s (x, p). This is done by commuting the Jacobi equation (15) and showing that the important structure described above is preserved. The Jacobi fields which are used, and hence the vectors V used to take derivatives of f , have to be carefully chosen.…”

Section: 14mentioning

confidence: 99%

The Global Nonlinear Stability of Minkowski Space for the Massless Einstein–Vlasov System

Taylor

2017

Ann. PDE

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Minkowski space is shown to be globally stable as a solution to the EinsteinVlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving a small data semi-global existence result for the characteristic initial value problem for the massless Einstein-Vlasov system in this region. This relies on weighted estimates for the solution which, for the Vlasov part, are obtained by introducing the Sasaki metric on the mass shell and estimating Jacobi fields with respect to this metric by geometric quantities on the spacetime. The stability of Minkowski space result for the vacuum Einstein equations is then appealed to for the remaining regions.

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Section: 14mentioning

confidence: 99%

The Global Nonlinear Stability of Minkowski Space for the Massless Einstein–Vlasov System

Taylor

2017

Ann. PDE

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“…Let us now consider the Riemann curvature, whose components satisfy [11][Appendix A] R a bcd = K (δ a c g bd − δ a d g bc ) ,…”

Section: Cosmic No-hairmentioning

confidence: 99%

“…The Gaussian curvature of the surfaces of fixed angular coordinates is given by [11][Appendix A] K = 4Ω −2 ∂ũ∂ṽ logΩ .…”

Section: Cosmic No-hairmentioning

confidence: 99%

Cosmic No-Hair in Spherically Symmetric Black Hole Spacetimes

Costa

Natário

Oliveira

2019

Ann. Henri Poincaré

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We analyze in detail the geometry and dynamics of the cosmological region arising in spherically symmetric black hole solutions of the Einstein-Maxwell-scalar field system with a positive cosmological constant. More precisely, we solve, for such a system, a characteristic initial value problem with data emulating a dynamic cosmological horizon. Our assumptions are fairly weak, in that we only assume that the data approaches that of a subextremal Reissner-Nordström-de Sitter black hole, without imposing any rate of decay. We then show that the radius (of symmetry) blows up along any null ray parallel to the cosmological horizon ("near" i + ), in such a way that r = +∞ is, in an appropriate sense, a spacelike hypersurface. We also prove a version of the Cosmic No-Hair Conjecture by showing that in the past of any causal curve reaching infinity both the metric and the Riemann curvature tensor asymptote to those of a de Sitter spacetime. Finally, we discuss conditions under which all the previous results can be globalized.

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“…In this paper we examine the behavior of the renormalized Hawking mass ̟ (see (13)) and the scalar field at the Cauchy horizon. Depending on the control that we have on these quantities, we are able to construct extensions of the metric beyond the Cauchy horizon with different degrees of regularity.…”

Section: Introductionmentioning

confidence: 99%

On the Global Uniqueness for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant: Part 3. Mass Inflation and Extendibility of the Solutions

et al. 2017

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This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the EinsteinMaxwell-scalar field system with a cosmological constant Λ, with the data on the outgoing initial null hypersurface given by a subextremal ReissnerNordström black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold.In the first part [7] of this series we established the well posedness of the characteristic problem, whereas in the second part [8] we studied the stability of the radius function at the Cauchy horizon.In this third and final paper we show that, depending on the decay rate of the initial data, mass inflation may or may not occur. When the mass is controlled, it is possible to obtain continuous extensions of the metric across the Cauchy horizon with square integrable Christoffel symbols. Under slightly stronger conditions, we can bound the gradient of the scalar field. This allows the construction of (non-isometric) extensions of the maximal development which are classical solutions of the Einstein equations. Our results provide evidence against the validity of the strong cosmic censorship conjecture when Λ > 0.

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Strong Cosmic Censorship for Surface‐Symmetric Cosmological Spacetimes with Collisionless Matter

Cited by 26 publications

References 62 publications

The Global Nonlinear Stability of Minkowski Space for the Massless Einstein–Vlasov System

The Global Nonlinear Stability of Minkowski Space for the Massless Einstein–Vlasov System

Cosmic No-Hair in Spherically Symmetric Black Hole Spacetimes

On the Global Uniqueness for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant: Part 3. Mass Inflation and Extendibility of the Solutions

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