Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-06-24
Phys.Rev. D69 (2004) 104028
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Uses revtex4. V2: Minor clarifications, plus an additional section on how to turn the algorithm into a solution generalization
Scientific paper
10.1103/PhysRevD.69.104028
Perfect fluid spheres, both Newtonian and relativistic, have attracted considerable attention as the first step in developing realistic stellar models (or models for fluid planets). Whereas there have been some early hints on how one might find general solutions to the perfect fluid constraint in the absence of a specific equation of state, explicit and fully general solutions of the perfect fluid constraint have only very recently been developed. In this article we present a version of Lake's algorithm [Phys. Rev. D 67 (2003) 104015; gr-qc/0209104] wherein: (1) we re-cast 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 formulae 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 inter-relationships among many of the previously known exact solutions, and generate several new exact solutions.
Martin Damien
Visser Matt
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