Studying conformally flat spacetimes with an elastic stress energy tensor using 1+3 formalism
Mathematical Physics
2015-01-13 v2 General Relativity and Quantum Cosmology
math.MP
Abstract
Conformally flat spacetimes with an elastic stress energy tensor given by a diagonal trace-free anisotropic pressure tensor are investigated using 1+3 formalism. We show how the null tetrad Ricci components are related to the pressure components and energy density. The 1+3 Bianchi and Jacobi identities and Einstein field equations are written for this particular case. In general the commutators must be considered since they supply potentially new information on higher order derivatives of the 1+3 quantities. We solve the system for the non rotating case which consist of ODEs of a spatial coordinate.
Keywords
Cite
@article{arxiv.1205.6723,
title = {Studying conformally flat spacetimes with an elastic stress energy tensor using 1+3 formalism},
author = {I. Brito and M. P. Machado Ramos},
journal= {arXiv preprint arXiv:1205.6723},
year = {2015}
}