Algorithmic construction of static perfect fluid spheres
- 27 May 2004
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 69 (10), 104028
- https://doi.org/10.1103/physrevd.69.104028
Abstract
Perfect fluid spheres, either Newtonian or relativistic, are the first step in developing realistic stellar models (or models for fluid planets). Despite the importance of these models, explicit and fully general solutions of the perfect fluid constraint in general relativity have only very recently been developed. In this paper we present a variant of Lake’s algorithm wherein (1) we recast the algorithm in terms of variables with a clear physical meaning—the average density and the locally measured acceleration due to gravity, (2) we present explicit and fully general formulas for the mass profile and pressure profile, and (3) we present an explicit closed-form expression for the central pressure. Furthermore we can then use the formalism to easily understand the pattern of interrelationships among many of the previously known exact solutions, and generate several new exact solutions.Keywords
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This publication has 8 references indexed in Scilit:
- All static spherically symmetric perfect-fluid solutions of Einstein’s equationsPhysical Review D, 2003
- Spacetime geometry of static fluid spheresClassical and Quantum Gravity, 2002
- Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein's equationsComputer Physics Communications, 1998
- General exact solutions of Einstein equations for static perfect fluids with spherical symmetryJournal of Mathematical Physics, 1987
- General Relativistic Fluid Spheres. II. General Inequalities for Regular SpheresThe Astrophysical Journal, 1966
- General Relativistic Fluid SpheresPhysical Review B, 1959
- Radially Symmetric Distributions of MatterPhysical Review B, 1949
- Spherically Symmetrical Models in General RelativityMonthly Notices of the Royal Astronomical Society, 1947