Remarks on the existence of CMC Cauchy surfaces

Galloway, Gregory J.; Ling, Eric

doi:10.48550/arxiv.2104.02136

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2021

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“…To our knowledge, these results are new and have not appeared elsewhere in the literature. There are nonetheless some recent results in [35] of a similar flavor. In their work, it is shown that conformal rescalings of a class of generalized Robertson-Walker spacetimes must introduce geodesic incompleteness when requiring the strong energy condition.…”

Section: Discussionmentioning

confidence: 95%

Conformal rigidity from focusing

Folkestad¹,

Hernández-Cuenca²

2021

Class. Quantum Grav.

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The null curvature condition (NCC) is the requirement that the Ricci curvature of a Lorentzian manifold be nonnegative along null directions, which ensures the focusing of null geodesic congruences. In this paper, we show that the NCC together with the causal structure significantly constrain the metric. In particular, we prove that any conformal rescaling of a vacuum spacetime introduces either geodesic incompleteness or negative null curvature, provided the conformal factor is non-constant on at least one complete null geodesic. In the context of bulk reconstruction in anti-de Sitter/CFT, our results combined with the technique of light-cone cuts can be used in vacuum spacetimes to reconstruct the full metric in regions probed by complete null geodesics reaching the boundary. For non-vacuum spacetimes, our results constrain the conformal factor, giving an approximate reconstruction of the metric.

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Section: Discussionmentioning

confidence: 95%