Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
L. HerreraEscuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, VenezuelaJ. OspinoArea de Física Teórica, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, SpainA. Di PriscoEscuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, VenezuelaE. FuenmayorEscuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, VenezuelaO. TroconisEscuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, Venezuela
2009en
ABI
Abstract
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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