Astrophysical applications of the post-Tolman-Oppenheimer-Volkoff   formalism
  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. 
Kostas Glampedakis, George Pappas, Hector O. Silva, Emanuele Berti
gr-qc astro-ph.HE