Naked Singularities for the Einstein Vacuum Equations: The Interior Solution
General Relativity and Quantum Cosmology
2022-04-22 v1 Mathematical Physics
Analysis of PDEs
Differential Geometry
math.MP
Abstract
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which corresponded to the exterior region of a naked singularity. In this work we construct solutions which correspond to the interior region and show that the two solutions may be glued together to produce a naked singularity. Fundamental to our construction is the novel type of self-similarity for the Einstein vacuum equations that we introduced in our previous work and also the study of a new class of quasilinear PDE's of mixed degenerate elliptic-hyperbolic type.
Keywords
Cite
@article{arxiv.2204.09891,
title = {Naked Singularities for the Einstein Vacuum Equations: The Interior Solution},
author = {Yakov Shlapentokh-Rothman},
journal= {arXiv preprint arXiv:2204.09891},
year = {2022}
}
Comments
166 pages, 5 figures