Action Principle for Isotropic General Relativity
Aug 30, 2018Citations per year
Abstract: (arXiv)
We study the generally covariant theory governing an isotropic spacetime region with uniform energy density. Gibbons, Hawking and York showed that fixing the induced boundary metric yields a well-posed variational problem. However, as we demonstrate, fixing the boundary metric violates general covariance and allows the mass of a back hole to vary. This observation has dramatic consequences for path integrals: A sum over spacetimes with fixed boundary metrics is a sum over classically distinct black holes. Instead, we merely demand that coordinates exist such that the metric at the boundary is the Schwarzschild-(A)dS metric of fixed mass M and two-sphere radius R. We derive the action that yields a well-posed variational problem for these physical boundary conditions. The action vanishes for all stationary and isotropic spacetimes. A vanishing action implies that both a Schwarzschild black hole and pure de Sitter space each have one unique semiclassical state. Our results provide a novel and radically conservative approach to several long-standing issues in quantum gravity, such as the wavefunction of the universe, the black hole information paradox, vacuum decay rates and the measure problem of eternal inflation.Note:
- 30 pages, 3 figures
- black hole: information theory
- black hole: Schwarzschild
- space: de Sitter
- energy: density
- space-time
- variational
- covariance
- boundary condition
- general relativity
- conservation law
References(33)
Figures(3)
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