Invariant construction of solutions to Einstein`s field equations - LRS perfect fluids I

Details Invariant construction of solutions to Einstein`s field equations - LRS perfect fluids I Invariant construction of solutions to Einstein`s field equations - LRS perfect fluids I

1996-12-05

arxiv.org/abs/gr-qc/9612014v1

Class.Quant.Grav. 14 (1997) 1267-1284

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, LaTeX (uses ioplppt)

Scientific paper

10.1088/0264-9381/14/5/028

The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives for finding solutions to Einstein's field equations. A new method is introduced, which makes it possible to choose the coordinates at any stage of the calculations. Three classes are examined, one with fluid rotation, one with spatial twist in the preferred direction and the space-time homogeneous models. It is also shown that there are no LRS space-times with dependence on one null coordinate. Using an extension of the method, we find the full metric in terms of curvature quantities for the first two classes.

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