Solution generating theorems for perfect fluid spheres

Abstract

The first static spherically symmetric perfect fluid solution with constant density was found by Schwarzschild in 1918. Generically, perfect fluid spheres are interesting because they are first approximations to any attempt at building a realistic model for a general relativistic star. Over the past 90 years a confusing tangle of specific perfect fluid spheres has been discovered, with most of these examples seemingly independent from each other. To bring some order to this collection, we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres. In addition, we develop new ``solution generating'' theorems for the TOV, whereby any given solution can be ``deformed'' to a new solution. Because these TOV-based theorems work directly in terms of the pressure profile and density profile it is relatively easy to impose regularity conditions at the centre of the fluid sphere.

8 pages, no figures, to appear in the proceedings of the NEB XII Conference (Recent Developments in Gravity), 29 June - 2 July, 2006, Napflio, Greece

References in corpus (6)

• Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
• All static spherically symmetric perfect fluid solutions of Einstein's Equations
• Generating perfect fluid spheres in general relativity
• Spacetime geometry of static fluid spheres
• Algorithmic construction of static perfect fluid spheres
• Bounds on the interior geometry and pressure profile of static fluid spheres

Cited by in corpus (8)

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• Decomposition of total stress-energy for the generalised Kiselev black hole
• Modelling anisotropic fluid spheres in general relativity
• Buchdahl-like transformations for perfect fluid spheres
• Transforming the Einstein static Universe into physically acceptable static fluid spheres
• The Navier-Stokes equation and solution generating symmetries from holography