Emergent Time in Hamiltonian General Relativity
Abstract
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 dimensions with 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.
Cite
@article{arxiv.2405.18486,
title = {Emergent Time in Hamiltonian General Relativity},
author = {Anurag Kaushal and Naveen S. Prabhakar and Spenta R. Wadia},
journal= {arXiv preprint arXiv:2405.18486},
year = {2024}
}
Comments
Minor corrections, references updated