2018/08/30 by Thomas C. Bachlechner, Bachlechner, Thomas C. · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1808.10448
30 pages, 3 figures
arxiv created 2018/08/30 · openalex publication_date 2018/08/30 · arxiv updated 2018/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.