Test-particle dynamics in general spherically symmetric black hole spacetimes

TL;DR

This paper develops a mathematical framework for test-particle dynamics in spherically symmetric black hole spacetimes, enabling precise predictions of orbital parameters and enhancing tests of gravity theories near black holes.

Contribution

It introduces a general analytic approach to describe test-particle motion in spherically symmetric black hole spacetimes, applicable to various gravity theories and astrophysical scenarios.

Findings

Derived analytic expressions for periastron advance and orbital period.

Applied framework to black hole solutions in general relativity and alternative theories.

Showed pulsar observations can better constrain gravity theories.

Abstract

To date, the most precise tests of general relativity have been achieved through pulsar timing, albeit in the weak-field regime. Since pulsars are some of the most precise and stable "clocks" in the Universe, present observational efforts are focused on detecting pulsars in the vicinity of supermassive black holes (most notably in our Galactic Centre), enabling pulsar timing to be used as an extremely precise probe of strong-field gravity. In this paper a mathematical framework to describe test-particle dynamics in general black hole spacetimes is presented, and subsequently used to study a binary system comprising a pulsar orbiting a black hole. In particular, taking into account the parameterization of a general spherically symmetric black hole metric, general analytic expressions for both the advance of the periastron and for the orbital period of a massive test particle are derived. Furthermore, these expressions are applied to four representative cases of solutions arising in both general relativity and in alternative theories of gravity. Finally, this framework is applied to the Galactic Centre $S$-stars and four distinct pulsar toy models. It is shown that by adopting a fully general-relativistic description of test-particle motion which is independent of any particular theory of gravity, observations of pulsars can help impose better constraints on alternative theories of gravity than is presently possible.