Post-Tolman-Oppenheimer-Volkoff formalism for relativistic stars

TL;DR

This paper introduces a parametrized formalism for modeling relativistic stars that captures deviations from general relativity without relying on specific alternative gravity theories, aiding in understanding neutron star properties.

Contribution

It develops a generalized stellar structure formalism inspired by PPN theory, extending TOV equations with correction terms to describe deviations from GR in a theory-agnostic way.

Findings

Formalism modifies neutron star mass and radius predictions.

Equivalent to GR with an effective equation of state.

Provides a simple parametrized approach to test gravity theories.

Abstract

Besides their astrophysical interest, compact stars also provide an arena for understanding the properties of theories of gravity that differ from Einstein's general relativity. Numerous studies have shown that different modified theories of gravity can modify the bulk properties (such as mass and radius) of neutron stars for given assumptions on the microphysics. What is not usually stressed though is the strong degeneracy in the predictions of these theories for the stellar mass and radius. Motivated by this observation, in this paper we take an alternative route and construct a stellar structure formalism which, without adhering to any particular theory of gravity, describes in a simple parametrized form the departure from compact stars in general relativity. This "post-Tolman-Oppenheimer-Volkoff (TOV)" formalism for spherical static stars is inspired by the well-known parametrized post-Newtonian theory, extended to second post-Newtonian order by adding suitable correction terms to the fully relativistic TOV equations. We show how neutron star properties are modified within our formalism, paying special attention to the effect of each correction term. We also show that the formalism is equivalent to general relativity with an "effective" (gravity-modified) equation of state.