New parametrization for spherically symmetric black holes in metric theories of gravity

TL;DR

This paper introduces a novel parametrization method for spherically symmetric black holes in metric theories of gravity using continued-fraction expansion, improving convergence and efficiency over previous approaches.

Contribution

A new parametrization framework employing continued-fraction expansion for spherically symmetric black holes in metric theories of gravity, enhancing approximation accuracy and observational constraints.

Findings

Superior convergence properties demonstrated.

Efficient approximation of known metric theories.

Potential for constraining gravity theories via near-horizon observations.

Abstract

We propose a new parametric framework to describe in generic metric theories of gravity the spacetime of spherically symmetric and slowly rotating black holes. In contrast to similar approaches proposed so far, we do not use a Taylor expansion in powers of M/r, where M and r are the mass of the black hole and a generic radial coordinate, respectively. Rather, we use a continued-fraction expansion in terms of a compactified radial coordinate. This choice leads to superior convergence properties and allows us to approximate a number of known metric theories with a much smaller set of coefficients. The measure of these coefficients via observations of near-horizon processes can be used to effectively constrain and compare arbitrary metric theories of gravity. Although our attention is here focussed on spherically symmetric black holes, we also discuss how our approach could be extended to rotating black holes.