Exact general relativistic thick disks

Guillermo A. González and Patricio S. Letelier
Phys. Rev. D 69, 044013 – Published 20 February 2004
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Abstract

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, 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 the 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 nontrivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied.

  • Received 10 September 2003

DOI:https://doi.org/10.1103/PhysRevD.69.044013

©2004 American Physical Society

Authors & Affiliations

Guillermo A. González*

  • Escuela de Física, Universidad Industrial de Santander, A. A. 678, Bucaramanga, Colombia

Patricio S. Letelier

  • Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas, 13081-970 Campinas, S.P., Brazil

  • *Email address: guillego@uis.edu.co
  • Email address: letelier@ime.unicamp.br

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Vol. 69, Iss. 4 — 15 February 2004

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