Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations

Details Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations

1998-09-02

arxiv.org/abs/gr-qc/9809013v1

Comput.Phys.Commun.115:395-415,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages. To appear in Computer Physics Communications Thematic Issue on "Computer Algebra in Physics Research"

Scientific paper

10.1016/S0010-4655(98)00130-1

We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate solutions were subjected to the following elementary tests: i) isotropy of the pressure, ii) regularity at the origin, iii) positive definiteness of the energy density and pressure at the origin, iv) vanishing of the pressure at some finite radius, v) monotonic decrease of the energy density and pressure with increasing radius, and vi) subluminal sound speed. A total of 127 candidate solutions were found. Only 16 of these passed all the tests. Of these 16, only 9 have a sound speed which monotonically decreases with radius. The analysis was facilitated by use of the computer algebra system GRTensorII.

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