Relativistic polytropic equations of state in Ho\v{r}ava gravity and Einstein-\ae ther theory

TL;DR

This paper investigates the equations of state for anisotropic fluids within spherically symmetric solutions in Horava gravity and Einstein-aether theory, deriving modified polytropic relations to match density and pressure profiles.

Contribution

It introduces a method to derive and modify relativistic polytropic equations of state for anisotropic fluids in alternative gravity theories using exact solutions.

Findings

Relativistic polytropic equations of state are adapted for anisotropic fluids.

Modified equations of state better fit the density and pressure profiles.

Analytical solutions inform the thermodynamical structure of stellar objects.

Abstract

The equations of state for a characteristic spacetime are studied in the context of the spherically symmetric interior exact and analytical solutions in Horava gravity and Einstein-aether theory in which anisotropic fluids are considered. In particular, for a given anisotropic interior solution, the equations of state relating the density to the radial and tangential pressure are derived, by means of a polynomial best-fit. Moreover, the well-known relativistic polytropic equations of state are used in order to obtain the profile of the thermodynamical quantities inside the stellar object as provided by the specific exact solution considered. It is then shown that these equations of state need to be modified in order to account for the profiles of density and pressures.