Surface Gravity of Compact Non-degenerate Horizons Under the Dominant Energy Condition

Gurriaran, Sebastian; Minguzzi, E.

doi:10.1007/s00220-022-04440-8

Commun. Math. Phys.

2022

DOI: 10.1007/s00220-022-04440-8

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Surface Gravity of Compact Non-degenerate Horizons Under the Dominant Energy Condition

Sebastian Gurriaran

E. Minguzzi

Abstract: We prove that under the dominant energy condition any non-degenerate smooth compact totally geodesic horizon admits a smooth tangent vector field of constant non-zero surface gravity. This result generalizes previous work by Isenberg and Moncrief, and by Bustamante and Reiris to the non-vacuum case, the vacuum case being given a largely independent proof. Moreover, we prove that any such achronal non-degenerate horizon is actually a Cauchy horizon bounded on one side by a chronology violating region.

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Cited by 4 publications

References 46 publications

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Symmetries of Vacuum Spacetimes with a Compact Cauchy Horizon of Constant Nonzero Surface Gravity

Petersen

Rácz

2023

Ann. Henri Poincaré

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We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a nonzero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983 under the assumption on the surface gravity and generalises previous results due to Moncrief–Isenberg and Friedrich–Rácz–Wald, where the generators of the Cauchy horizon were closed or densely filled a 2-torus. Consequently, the maximal globally hyperbolic vacuum development of generic initial data cannot be extended across a compact Cauchy horizon with surface gravity that can be normalised to a nonzero constant. Our result supports, thereby, the validity of the strong cosmic censorship conjecture in the considered special case. The proof consists of two main steps. First, we show that the Killing equation can be solved up to infinite order at the Cauchy horizon. Second, by applying a recent result of the first author on wave equations with initial data on a compact Cauchy horizon, we show that this Killing vector field extends to the globally hyperbolic region.

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Symmetries of Vacuum Spacetimes with a Compact Cauchy Horizon of Constant Nonzero Surface Gravity

Petersen

Rácz

2023

Ann. Henri Poincaré

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The Asymptotic Expansion of the Spacetime Metric at the Event Horizon

Kröncke,

Petersen

2024

Ann. Henri Poincaré

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Hawking’s local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full asymptotic expansion of any smooth vacuum metric at a non-degenerate Killing horizon is determined by the geometry of the horizon. This gives a new perspective on the black hole uniqueness conjecture. In spacetime dimension 4, we also prove an existence theorem: Given any non-degenerate horizon geometry, Einstein’s vacuum equations can be solved to infinite order at the horizon in a unique way (up to isometry). The latter is a gauge invariant version of Moncrief’s classical existence result, without any restriction on the topology of the horizon. In the real analytic setting, the asymptotic expansion is shown to converge and we get well-posedness of this characteristic Cauchy problem.

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Analyticity of Quasinormal Modes in the Kerr and Kerr–de Sitter Spacetimes

Petersen

Vasy

2023

Commun. Math. Phys.

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We prove that quasinormal modes (or resonant states) for linear wave equations in the subextremal Kerr and Kerr–de Sitter spacetimes are real analytic. The main novelty of this paper is the observation that the bicharacteristic flow associated to the linear wave equations for quasinormal modes with respect to a suitable Killing vector field has a stable radial point source/sink structure rather than merely a generalized normal source/sink structure. The analyticity then follows by a recent result in the microlocal analysis of radial points by Galkowski and Zworski. The results can then be recast with respect to the standard Killing vector field.

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Surface Gravity of Compact Non-degenerate Horizons Under the Dominant Energy Condition

Cited by 4 publications

References 46 publications

Symmetries of Vacuum Spacetimes with a Compact Cauchy Horizon of Constant Nonzero Surface Gravity

Symmetries of Vacuum Spacetimes with a Compact Cauchy Horizon of Constant Nonzero Surface Gravity

The Asymptotic Expansion of the Spacetime Metric at the Event Horizon

Analyticity of Quasinormal Modes in the Kerr and Kerr–de Sitter Spacetimes

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