Isothermal spheres in general relativity and Horava-type gravity

TL;DR

This paper develops a toy model for isothermal spheres within Horava gravity, demonstrating its consistency with Einstein gravity in certain limits and analyzing the stability based on central energy density.

Contribution

It introduces a novel toy model for isothermal spheres in Horava gravity, connecting it to Einstein gravity and analyzing stability criteria.

Findings

Model reduces to Einstein gravity in specific parameter limits.

Newtonian limit matches the classical isothermal sphere.

Stability depends on the central energy density.

Abstract

We construct a toy model for isothermal spheres in Horava gravity, which includes Einstein's gravity if a parameter is appropriately chosen. The equations for the isothermal spheres are derived from the partition function of the gravitating particle system. We confirm that the Newtonian limit of the system coincides with the model of the well-known isothermal sphere. The stability of the isothermal sphere is found to be sensitive to the energy density at the center of the sphere.