Neutral perfect fluids of Majumdar-type in general relativity

TL;DR

This paper extends Majumdar-type solutions in general relativity to include neutral perfect fluids with a specific equation of state, revealing unique gravitational properties and potential for broader applications.

Contribution

It introduces a new class of static solutions with neutral perfect fluids satisfying $ ho+3p=0$, expanding the Majumdar-type solutions to include charged shells and exotic geometries.

Findings

Neutral perfect fluid solutions with $ ho+3p=0$ are constructed.

The solutions feature a condenser-like geometry with flat and Schwarzschild regions.

The fluid exhibits an exotic gravitational property.

Abstract

We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations, proposed by Ida to include charged perfect fluid sources. We impose the equation of state $\rho+3p=0$ and discuss spherically symmetric solutions for the linear potential equation satisfied by the metric. In this particular case the fluid charge density vanishes and we locate the arising neutral perfect fluid in the intermediate region defined by two thin shells with respective charges $Q$ and $-Q$. With its innermost flat and external (Schwarzschild) asymptotically flat spacetime regions, the resultant condenser-like geometries resemble solutions discussed by Cohen and Cohen in a different context. We explore this relationship and point out an exotic gravitational property of our neutral perfect fluid. We mention possible continuations of this study to embrace non-spherically symmetric situations and higher dimensional spacetimes.