Gravitational Observatories
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908486930006016 |
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| author | Anninos, Dionysios Galante, Damián A. Maneerat, Chawakorn |
| author_facet | Anninos, Dionysios Galante, Damián A. Maneerat, Chawakorn |
| contents | 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 $\boldsymbolσ \times \mathbb{R}$, with $\boldsymbolσ$ a spatial two-manifold that we take to be either flat or $S^2$. In Euclidean signature, we take the boundary to be $S^2\times S^1$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08648 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gravitational Observatories Anninos, Dionysios Galante, Damián A. Maneerat, Chawakorn High Energy Physics - Theory General Relativity and Quantum Cosmology 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 $\boldsymbolσ \times \mathbb{R}$, with $\boldsymbolσ$ a spatial two-manifold that we take to be either flat or $S^2$. In Euclidean signature, we take the boundary to be $S^2\times S^1$. 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. |
| title | Gravitational Observatories |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2310.08648 |