Astrophysical applications of the post-Tolman-Oppenheimer-Volkoff formalism

TL;DR

This paper extends a formalism for analyzing deviations from general relativity in compact stars to their exterior, enabling the calculation of observable quantities that depend on modified gravity parameters.

Contribution

The authors expand the post-TOV formalism to include stellar exterior effects and identify key observables sensitive to deviations from GR.

Findings

Surface redshift and apparent radius depend on two post-TOV parameters.

Potential to measure or constrain deviations from GR using astrophysical observations.

Formalism simplifies to depend on just two parameters at leading order.

Abstract

The bulk properties of spherically symmetric stars in general relativity can be obtained by integrating the Tolman-Oppenheimer-Volkoff (TOV) equations. In previous work we developed a "post-TOV" formalism - inspired by parametrized post-Newtonian theory - which allows us to classify in a parametrized, phenomenological form all possible perturbative deviations from the structure of compact stars in general relativity that may be induced by modified gravity at second post-Newtonian order. In this paper we extend the formalism to deal with the stellar exterior, and we compute several potential astrophysical observables within the post-TOV formalism: the surface redshift $z_s$, the apparent radius $R_{\rm app}$, the Eddington luminosity at infinity $L_{\rm E}^\infty$ and the orbital frequencies. We show that, at leading order, all of these quantities depend on just two post-TOV parameters $\mu_1$ and $\chi$, and we discuss the possibility to measure (or set upper bounds on) these parameters.