Generating static perfect-fluid solutions of Einstein's equations

TL;DR

This paper introduces a transformation-based method to generate exact static, axially symmetric perfect-fluid solutions in Einstein's equations, expanding the set of known interior solutions with distinct physical properties.

Contribution

It develops a new transformation technique that generates interior solutions from seed solutions, generalizing the Zipoy-Voorhees transformation to perfect-fluid spacetimes.

Findings

Explicit formulas for new solutions derived from seed solutions.

New solutions exhibit different physical properties from seed solutions.

Method reduces to Zipoy-Voorhees transformation in vacuum case.

Abstract

We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well as the density and pressure of the seed solution. In the limiting vacuum case, it reduces to the Zipoy-Voorhees transformation that can be used to generate metrics with multipole moments. All the metric functions of the new solution can be calculated explicitly from the seed solution in a simple manner. The physical properties of the resulting new solutions are shown to be completely different from those of the seed solution.