2023/11/12 by Quentin Vigneron, Vigneron, Quentin, Áron Szabó +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2311.06927
openalex publication_date 2023/11/12 · openalex created_date 2023/11/15 · openalex updated_date 2026/07/28
Vigneron [Foundations of Physics, 54, 15, (2024)] recently proposed a modification of general relativity in which a non-dynamical term related to the spatial topology is introduced in the Einstein equation. The original motivation for this theory is to allow for the non-relativistic limit to exist in any physical topology. In the present paper, we derive a first inhomogeneous exact vacuum solution of this theory for a spherical topology, assuming staticity and spherical symmetry. The metric represents a black hole and a repulsive singularity at opposite poles of a 3-sphere. The solution is similar to the Schwarzschild metric, but the spacelike infinity is cut, and replaced by a repulsive singularity at finite distance, implying that the spacelike hypersurfaces have finite volume, and the total mass is zero. We discuss how this solution paves the way to massive, non-static solutions of this theory, more directly relevant for cosmology.