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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.18486 |
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| _version_ | 1866913536774504448 |
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| author | Kaushal, Anurag Prabhakar, Naveen S. Wadia, Spenta R. |
| author_facet | Kaushal, Anurag Prabhakar, Naveen S. Wadia, Spenta R. |
| contents | In this paper we introduce a definition of time that emerges in terms of the geometry of the configuration space of a dynamical system. We illustrate this, using the Hamilton-Jacobi equation, in various examples: particle mechanics on a fixed energy surface; non-Abelian gauge theories for compact semi-simple Lie groups where the Gauss law presents new features; and General Relativity in $d+1$ dimensions with $d$ the dimension of space. The discussion in General Relativity is like the non-abelian gauge theory case except for the indefiniteness of the de Witt metric in the Einstein-Hamilton-Jacobi equation, which we discuss in some detail. We illustrate the general formula for the emergent time in various examples including de Sitter spacetime and asymptotically AdS spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emergent Time in Hamiltonian General Relativity Kaushal, Anurag Prabhakar, Naveen S. Wadia, Spenta R. High Energy Physics - Theory General Relativity and Quantum Cosmology In this paper we introduce a definition of time that emerges in terms of the geometry of the configuration space of a dynamical system. We illustrate this, using the Hamilton-Jacobi equation, in various examples: particle mechanics on a fixed energy surface; non-Abelian gauge theories for compact semi-simple Lie groups where the Gauss law presents new features; and General Relativity in $d+1$ dimensions with $d$ the dimension of space. The discussion in General Relativity is like the non-abelian gauge theory case except for the indefiniteness of the de Witt metric in the Einstein-Hamilton-Jacobi equation, which we discuss in some detail. We illustrate the general formula for the emergent time in various examples including de Sitter spacetime and asymptotically AdS spacetimes. |
| title | Emergent Time in Hamiltonian General Relativity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.18486 |