Generating spherically symmetric static perfect fluid solutions

TL;DR

This paper introduces a new algebraic method using variable transformations to generate and analyze spherically symmetric static perfect fluid solutions, ensuring physical regularity and providing explicit examples.

Contribution

It develops a novel algebraic approach to solve the pressure isotropy condition for perfect fluids using variable transformations, enabling explicit solution generation.

Findings

Two physically well-behaved solutions are constructed.

Conditions for regularity and physicality near the center are established.

Explicit models include a compact fluid sphere and an infinite sphere.

Abstract

By a choice of new variables the pressure isotropy condition for spherically symmetric static perfect fluid spacetimes can be made a quadratic algebraic equation in one of the two functions appearing in it. Using the other variable as a generating function, the pressure and the density of the fluid can be expressed algebraically by the function and its derivatives. One of the functions in the metric can also be expressed similarly, but to obtain the other function, related to the redshift factor, one has to perform an integral. Conditions on the generating function ensuring regularity and physicality near the center are investiagted. Two everywhere physically well behaving example solutions are generated, one representing a compact fluid body with a zero pressure surface, the other an infinite sphere.