Geodesics, complexity and holography in (A)dS_2

Galante, Damián A.

doi:10.22323/1.406.0359

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…Notably, we see that all these symmetric geodesics have the same geodesic length, in other words the length is independent of E. As also pointed out in [39,40], even in the limit E → ∞, the geodesic length remains πℓ. This could be considered surprising as one typically expects spacelike geodesics to become null in this limit.…”

Section: Jcap05(2024)118supporting

confidence: 67%

“…When the conserved quantity E approaches infinity, the spacelike geodesics from the north pole at τ N = 0 get ever closer to future infinity before they turn around and reach the south pole at τ S = 0. For any other (symmetric) time, no (real) spacelike geodesics exist that connect two conjugate points [40,46]. As our analysis of the SdS causal structure has shown, introducing a black hole in de Sitter significantly affects the above situation for a pair of conjugate static sphere observers.…”

Section: Spacelike Geodesics Between Static Sphere Observers In Sdsmentioning

confidence: 87%

“…times) on the two poles. Instead, as shown in [37,40], one needs to introduce complex geodesics in order to connect symmetric points on the north and south pole lying that are not located at τ = 0. This ends our introduction.…”

Section: Jcap05(2024)118mentioning

confidence: 99%

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Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

Faruk,

Morvan,

van der Schaar

2024

J. Cosmol. Astropart. Phys.

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We analyze null- and spacelike radial geodesics in Schwarzschild-de Sitter spacetime connecting two conjugate static sphere observers, i.e. free-falling observers at a fixed radius in between the two horizons. We explicitly determine the changes in the causal structure with respect to these natural observers as a result of the inward bending of the black hole singularity, as well as the outward bending of asymptotic infinity. Notably, the inward and outward bending changes as a function of the black hole mass, first increasing towards a maximum and then decreasing to vanish in the extreme Nariai limit. For a generic mass of the black hole this implies the existence of finite size (temporal) windows for the presence of symmetric radial geodesics between the static sphere observers probing the interior region of the black hole, as well as the exterior de Sitter region. We determine the size of the interior (black hole) and exterior (de Sitter) temporal windows in 4, 5 and 6 spacetime dimensions, finding that they are equal in D = 5, and compute the proper lengths of the symmetric radial geodesics. We comment on the implications for information exchange and the potential role of the symmetric radial geodesics in a geodesic approximation of static sphere correlators in Schwarzschild-de Sitter spacetime.

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Section: Jcap05(2024)118supporting

confidence: 67%

Section: Spacelike Geodesics Between Static Sphere Observers In Sdsmentioning

confidence: 87%

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Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

Faruk,

Morvan,

van der Schaar

2024

J. Cosmol. Astropart. Phys.

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“…There, it was also suggested that the double scaled Sachdev-Ye-Kitaev model [138] might have this feature. Several works have tried to make this relation more precise [139][140][141][142][143][144][145][146][147]; however, at the time of writing, the status of chaos and complexity in dS remains inconclusive [48,[148][149][150][151][152][153][154][155].…”

Section: Pos(modave2022)003mentioning

confidence: 99%

Modave lectures on de Sitter space & holography

Galante¹

2023

Proceedings of Modave Summer School in Mathematical Physics — PoS(Modave2022)

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These lecture notes provide an overview of different aspects of de Sitter space and their plausible holographic interpretations. We start with a general description of the classical spacetime. We note the existence of a cosmological horizon and its associated thermodynamic quantities, such as the Gibbons-Hawking entropy. We discuss geodesics and shockwave solutions, that might play a role in a holographic description of de Sitter. Finally, we discuss different approaches to quantum theories of de Sitter space, with an emphasis on recent developments in static patch holography.

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“…Based on the worldline formalism of quantum field theory, in the large mass limit one might expect that the correlator (36) is obtained by computing the length of a spacelike geodesic connecting the two points. However, there are no real, finite-length geodesics between the two points at T > 0 [67,68]. Instead, the oscillatory form of the correlator in the large mass limit ∆ ∆ ≫ 1-see the second line in equations ( 32) and ( 35)-suggests the existence of complex geodesics that might account for this two-point function.…”

Section: Spacelike Separationmentioning

confidence: 99%

Finite features of quantum de Sitter space

Anninos

Galante²,

Mühlmann³

2022

Class. Quantum Grav.

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We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of a black hole. We point out diﬀerences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS2×S2 space and a dS4 interior are compatible with the null energy condition, albeit with a non-standard decreasing radial size of S2. The putative holographic dual of an asymptotic AdS2 spacetime is comprised of a ﬁnite number of underlying degrees of freedom. From a Euclidean perspective we consider the gravitational path integral for ﬁelds over compact manifolds. In two-dimensions, we review Polchinski’s BRST localisation of Liouville theory and propose a supersymmetric extension of timelike Liouville theory which exhibits supersymmetric localisation. We speculate that localisation of the Euclidean gravitational path integral is a reﬂection of a ﬁnite number of degrees of freedom in a quantum de Sitter universe.

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Geodesics, complexity and holography in (A)dS_2

Cited by 8 publications

References 16 publications

Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

Modave lectures on de Sitter space & holography

Finite features of quantum de Sitter space

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