Two-fluid stellar objects in General Relativity: the covariant formulation

TL;DR

This paper develops a covariant framework for modeling static, spherically symmetric stellar objects containing two interacting fluids in General Relativity, deriving new solutions and extending existing theorems.

Contribution

It introduces a covariant 1+1+2 formulation for two-fluid stellar models and extends the generating theorem to generate two-fluid solutions from single-fluid solutions.

Findings

Derived covariant TOV equations for two-fluid systems.

Obtained new exact solutions for two-fluid stellar objects.

Extended the generating theorem to two-fluid cases.

Abstract

We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding Tolman-Oppenheimer-Volkoff (TOV) equations in covariant form in the isotropic, non-interacting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.