Exact General Relativistic Thick Disks

Details Exact General Relativistic Thick Disks Exact General Relativistic Thick Disks

2003-11-24

arxiv.org/abs/gr-qc/0311078v1

Phys.Rev. D69 (2004) 044013

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, RevTex, 9 eps figs. Accepted for publication in PRD

Scientific paper

10.1103/PhysRevD.69.044013

A method to construct exact general relativistic thick disks that is a simple generalization of the ``displace, cut and reflect'' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This generalization consists in the addition of a new step in the above mentioned method. The new method can be pictured as a ``displace, cut, {\it fill} and reflect'' method. In the Newtonian case, the method is illustrated in some detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable physical properties. In the relativistic case two solutions of the Weyl equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild metric in isotropic coordinates is employed to construct another family of thick disks. In all the considered cases we have non trivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied.

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