Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor

Details Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor

2009-03-20

arxiv.org/abs/0903.3532v1

Phys.Rev.D79:064025,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages, Latex

Scientific paper

10.1103/PhysRevD.79.064025

The full set of equations governing the structure and the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses, is written down in terms of five scalar quantities obtained from the orthogonal splitting of the Riemann tensor, in the context of general relativity. It is shown that these scalars are directly related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux and the active gravitational mass. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through these scalars. Some solutions are exhibited to illustrate this point.

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