Unified geometrical basis for the generalized Ehlers identities and Raychaudhuri equations
General Relativity and Quantum Cosmology
2017-10-31 v3 Mathematical Physics
math.MP
Abstract
It is shown that the timelike, spacelike and null versions of the Ehlers identity, as well as ensuing Raychaudhuri equations, might be all derived within a single geometrical approach based on the definition of the Riemann curvature tensor specified with respect to the corresponding congruence. Still, spacelike and null cases have a number of non-trivial peculiarities deserving special attention.
Keywords
Cite
@article{arxiv.1707.00862,
title = {Unified geometrical basis for the generalized Ehlers identities and Raychaudhuri equations},
author = {Eduard G. Mychelkin and Maxim A. Makukov},
journal= {arXiv preprint arXiv:1707.00862},
year = {2017}
}
Comments
Accepted in Reports on Mathematical Physics