Generating New Perfect-fluid Solutions From Known Ones II

TL;DR

This paper explores a transformation method for generating new perfect-fluid solutions in general relativity, focusing on specific conditions like barotropic equations of state and static spacetimes, and relates it to existing techniques.

Contribution

It extends previous work by analyzing a transformation for perfect-fluid solutions under new assumptions, connecting it to known methods like Buchdahl's transformation.

Findings

Transformation applicable for rho+3p=0 or static spacetimes

Recovers Buchdahl transformation in static case

Herlt's technique is a special case of this method

Abstract

The properties of a transformation previously considered for generating new perfect-fluid solutions from known ones are further investigated. It is assumed that the four-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the stationary Killing field are functionally related. This case is complementary to the case studied in our previous paper. The transformation can be applied to generate possibly new perfect-fluid solutions from known ones only for the case of barotropic equation of state rho+3p=0 or, alternatively, for the case of a static spacetime. For static spacetimes our method recovers the Buchdahl transformation. It is demonstrated, moreover, that Herlt's technique for constructing stationary perfect-fluid solutions from static ones is, actually, a special case of the method considered in the present paper.