$C^3$ matching for asymptotically flat spacetimes
General Relativity and Quantum Cosmology
2019-09-04 v1
Abstract
We propose a criterion for finding the minimum distance at which an interior solution of Einstein's equations can be matched with an exterior asymptotically flat solution. It is based upon the analysis of the eigenvalues of the Riemann curvature tensor and their first derivatives, implying differentiability conditions. The matching itself is performed by demanding continuity of the curvature eigenvalues across the matching surface. We apply the matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. Several perfect fluid solutions in Newton and Einstein gravity are tested.
Keywords
Cite
@article{arxiv.1901.01363,
title = {$C^3$ matching for asymptotically flat spacetimes},
author = {Antonio C. Gutiérrez-Piñeres and Hernando Quevedo},
journal= {arXiv preprint arXiv:1901.01363},
year = {2019}
}