Spherically symmetric isothermal fluids in $f(R,T)$ gravity

TL;DR

This paper explores isothermal fluid spheres in $f(R,T)$ gravity, finding stable, causal models that generalize Einstein's solutions and analyzing their properties under various conditions.

Contribution

It introduces exact solutions for isothermal fluids in $f(R,T)$ gravity, demonstrating their stability and causality, and compares them to Einstein's models.

Findings

Einstein models are unstable and acausal, while $f(R,T)$ models are stable and well-behaved.

A complete, exact stellar model is derived with a constant gravitational potential.

Dropping the density restriction with a linear equation of state yields a new exact solution.

Abstract

We analyze the isothermal property in static fluid spheres within the framework of the modified $f(R, T)$ theory of gravitation. The equation of pressure isotropy of the standard Einstein theory is preserved however, the energy density and pressure are expressed in terms of both gravitational potentials. Invoking the isothermal prescription requires that the isotropy condition assumes the role of a consistency condition and an exact model generalizing that of general relativity is found. Moreover it is found that the Einstein model is unstable and acausal while the $f(R, T)$ counterpart is well behaved on account of the freedom available through an additional coupling constant. The case of a constant spatial gravitational potential is considered and the complete model is determined. This model is markedly different from its Einstein counterpart which is known to be isothermal. Dropping the restriction on the density and imposing a linear barotropic equation of state generates an exact solution and consequently a stellar distribution as the vanishing of the pressure is possible and a boundary hypersurface exists. Finally we comment on the case of relaxing the equation of state but demanding an inverse square fall-off of the density - this case proves intractable.