Gravitational observatories

Dionysios Anninos; Damián A. Galante; Chawakorn Maneerat

doi:10.1007/JHEP12(2023)024

Gravitational observatories

Dionysios Anninos, Damián A. Galante, Chawakorn Maneerat^*

^*Corresponding author for this work

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Abstract

We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form σ × ℝ, with σ a spatial two-manifold that we take to be either flat or S ². In Euclidean signature we take the boundary to be S ² × S ¹. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace K of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on S ² with constant K, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying K. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

Original language	English
Article number	24
Journal	Journal of High Energy Physics
Volume	2023
Issue number	12
DOIs	https://doi.org/10.1007/JHEP12(2023)024
Publication status	Published - 4 Dec 2023

Keywords

AdS-CFT Correspondence
Black Holes
Classical Theories of Gravity
de Sitter space

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Gravitational observatories_ANNINOS_2023_GOLD VoR (CC BY)Final published version, 1.96 MBLicence: CC BY

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title = "Gravitational observatories",

abstract = "We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form σ × ℝ, with σ a spatial two-manifold that we take to be either flat or S 2. In Euclidean signature we take the boundary to be S 2 × S 1. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace K of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on S 2 with constant K, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying K. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.",

keywords = "AdS-CFT Correspondence, Black Holes, Classical Theories of Gravity, de Sitter space",

author = "Dionysios Anninos and Galante, {Dami{\'a}n A.} and Chawakorn Maneerat",

note = "Funding Information: It is a pleasure to acknowledge Vijay Balasubramanian, Bianca Dittrich, Pau Figueras, Chris Herzog, Diego Hofman, Luis Lehner, Hong Liu, and Beatrix M{\"u}hlmann for useful discussions. D.A. is funded by the Royal Society under the grant “The Atoms of a deSitter Universe”. The work of D.A.G. is funded by UKRI Stephen Hawking Fellowship “Quantum Emergence of an Expanding Universe”. D.A. and D.A.G. are further funded by STFC Consolidated grant ST/X000753/1. C.M. is funded by STFC under grant number ST/X508470/1. Publisher Copyright: {\textcopyright} 2023, The Author(s).",

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doi = "10.1007/JHEP12(2023)024",

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AU - Anninos, Dionysios

AU - Galante, Damián A.

AU - Maneerat, Chawakorn

N1 - Funding Information: It is a pleasure to acknowledge Vijay Balasubramanian, Bianca Dittrich, Pau Figueras, Chris Herzog, Diego Hofman, Luis Lehner, Hong Liu, and Beatrix Mühlmann for useful discussions. D.A. is funded by the Royal Society under the grant “The Atoms of a deSitter Universe”. The work of D.A.G. is funded by UKRI Stephen Hawking Fellowship “Quantum Emergence of an Expanding Universe”. D.A. and D.A.G. are further funded by STFC Consolidated grant ST/X000753/1. C.M. is funded by STFC under grant number ST/X508470/1. Publisher Copyright: © 2023, The Author(s).

PY - 2023/12/4

Y1 - 2023/12/4

N2 - We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form σ × ℝ, with σ a spatial two-manifold that we take to be either flat or S 2. In Euclidean signature we take the boundary to be S 2 × S 1. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace K of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on S 2 with constant K, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying K. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

AB - We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form σ × ℝ, with σ a spatial two-manifold that we take to be either flat or S 2. In Euclidean signature we take the boundary to be S 2 × S 1. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace K of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on S 2 with constant K, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying K. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

KW - AdS-CFT Correspondence

KW - Black Holes

KW - Classical Theories of Gravity

KW - de Sitter space

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U2 - 10.1007/JHEP12(2023)024

DO - 10.1007/JHEP12(2023)024

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SN - 1126-6708

VL - 2023

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 12

M1 - 24

ER -

Gravitational observatories

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