A new algorithm for anisotropic solutions

Details A new algorithm for anisotropic solutions A new algorithm for anisotropic solutions

2006-01-08

arxiv.org/abs/gr-qc/0601030v1

Pramana66:313-324,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, to appear in Pramana - J. Phys

Scientific paper

10.1007/BF02704387

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.

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