Theorems on gravitational time delay and related issues

By Sijie Gao, R. Wald. 2000

276 citations recorded by the source corpus.

Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set K, there exists another compact set K' such that for any p,qK', if there exists a `fastest null geodesic', γ, between p and q, then γ cannot enter K. As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any observer at sufficiently late times cannot have a particle horizon. The second theorem states that if a timelike conformal boundary can be attached to the spacetime such that the spacetime with boundary satisfies strong causality as well as a compactness condition, then any `fastest null geodesic' connecting two points on the boundary must lie entirely within the boundary. It follows from this theorem that generic perturbations of anti-de Sitter spacetime always produce a time delay relative to anti-de Sitter spacetime itself.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d682907182d13cda99c19b03788edf09e3de53bf

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Citations in the corpus

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, background): “Using the classical equations of motion, it is possible (at least perturbatively in the bulk coupling constants) to reconstruct the bulk state in WR from the bulk fields near DR [23, 58–66].”
Bulk curves from boundary data in holography (2013, background): “glement entropy, whose denition incorporates the constraints of the time-energy uncertainty relation. The correct generalization of (31) may oer a holographic interpretation of the focusing theorem [39]. The problem is related to identifying a holographic dual to a density matrix, which has been 14 ”
Proof of the Quantum Null Energy Condition (2015, background): “The NEC underlies the area theorems [1, 2] and singularity theorems [3–5], and many other results in general relativity [6–14].”
Causality constraints on corrections to the graviton three-point coupling (2014, background): “As argued in [26, 57], General Relativity with the null energy condition implies that this is obeyed.”
Extremal surfaces as bulk probes in AdS/CFT (2012, background): “This is however already guaranteed by the stronger bound ∆t ≥ ∆φ implied by a theorem of Gao & Wald [24] which states that (subject to certain energy conditions) one can’t propagate faster through the bulk than along the boundary.”
Averaged null energy condition from causality (2016, background): “1 The connection between causality and null energy is well known in the gravitational context (see for example [20, 21] and the references above) and in AdS/CFT (see for example [22, 23]).”
The AdS/CFT correspondence (2014, background): “That this does not happen was proved by Gao and Wald [40] who showed that physically sensible23 deformations of AdS would lead to a gravitational time delay (as 23 More precisely, [40] assume the bulk satisfies the null energy condition (and the null generic condition). opposed to time advance) of b”
The gravity dual of a density matrix (2012, result): “This follows from a result of Gao and Wald [10] that light rays through the bulk of a generic asymptotically AdS spacetime generally take longer to reach the antipodal point of the sphere than light rays along the boundary.”
The dS/CFT correspondence (2001, background): “Even when collapse does not occur, the presence of matter alters the causal structure [24].”
A Holographic View on Physics out of Equilibrium (2010, background): “51 As proved by [203], for certain wide class of spacetimes (including the present case of interest) with timelike conformal boundary, any fastest null geodesic connecting two points on the boundary must lie entirely within the boundary.”
Entwinement and the emergence of spacetime (2014, unknown): “The focusing theorem [18] states that in an asymptotically anti-de Sitter spacetime, the fastest null geodesic connecting two boundary points lies entirely on the boundary.”
Causality & holographic entanglement entropy (2014, methodology): “This theorem can be viewed as a generalization of the Gao-Wald theorem [14].”
The Holographic principle (2002, background): “2). If de Sitter space is not completely empty, the Penrose diagram will be deformed. In the asymptotic regions matter is diluted, but in the interior of the spacetime it can have signiﬁcant density. Gao and Wald (2000) showed under generic assumptions47 that the back-reaction of matter makes the he”
Causal holographic information (2012, background): “By the Gao-Wald theorem [25], within a fixed time set by the size of ♦A, the null geodesics which define the causal wedge cannot reach as far from the AdS boundary as they could in the pure AdS spacetime.”