Paczynski-Wiita-like potential for any static spherical black hole in metric theories of gravity

TL;DR

This paper generalizes the Paczynski-Wiita pseudo-Newtonian potential to any static, spherically symmetric black hole spacetime, including those from alternative gravity theories, highlighting the non-uniqueness of such potentials.

Contribution

It introduces a new, more general method for deriving pseudo-Newtonian potentials applicable to various static spherical black holes, expanding beyond the Schwarzschild case.

Findings

The new potential applies to black holes in alternative gravity theories.

The prescription differs significantly from previous approaches.

The association of pseudo-Newtonian potentials with black hole metrics is not unique.

Abstract

The pseudo-Newtonian potential of Paczynski and Wiita for particles orbiting a Schwarzschild black hole is generalized to arbitrary static and spherically symmetric spacetimes, including black hole solutions of alternative theories of gravity. In addition to being more general, our prescription differs substantially from a previous one in the literature, showing that even the association of a pseudo-Newtonian potential with a simple black hole metric is not unique.