Generating Static Fluid Spheres by Conformal Transformations

Abstract

We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic coordinates). Special cases include the Schwarzschild interior solution and the Einstein static universe. The process we consider involves solving two equations of the Riccati type coupled by a single generating function rather than a specification of one of the two metric functions.

4 pages revtex4, two figures, Final form to appear in Phys. Rev. D

References in corpus (7)

• All static spherically symmetric perfect fluid solutions of Einstein's Equations
• The Ultimate Energy Density of Observable Cold Matter
• Spacetime geometry of static fluid spheres
• Buchdahl-like transformations for perfect fluid spheres
• Transforming the Einstein static Universe into physically acceptable static fluid spheres
• Transforming the Einstein static Universe into physically acceptable static fluid spheres II: A two - fold infinity of exact solutions
• An inverse approach to Einstein's equations for non-conducting fluids

Cited by in corpus (6)

• Isotropic stars in general relativity
• Generating static spherically symmetric anisotropic solutions of Einstein's equations from isotropic Newtonian solutions
• Scalar Polynomial Curvature Invariant Vanishing on the Event Horizon of Any Black Hole Metric Conformal to a Static Spherical Metric
• Modelling anisotropic fluid spheres in general relativity
• Hawking-Hayward quasi-local energy under conformal transformations
• Static conformal elastic solution of Einstein's field equations