General parametrization of higher-dimensional black holes and its application to Einstein-Lovelock theory

TL;DR

This paper introduces a comprehensive parametrization method for higher-dimensional black holes in arbitrary gravity theories, enabling simplified analytic approximations of complex solutions with high accuracy, demonstrated on Einstein-Lovelock black holes.

Contribution

It generalizes the continued-fraction expansion approach to higher dimensions and arbitrary theories, providing a compact analytic form for black-hole solutions depending on multiple parameters.

Findings

Approximate metrics deviate less than 1% from exact solutions.

Method accurately reproduces observable quantities like quasinormal modes.

Applicable to Einstein-Lovelock black holes in various dimensions.

Abstract

Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian (PPN) approximation, but valid in the whole space outside the event horizon, including the near horizon region. This generalizes the continued-fraction expansion method in terms of a compact radial coordinate suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the four-dimensional case. As the first application of our higher-dimensional parametrization we have approximated black-hole solutions of the Einstein-Lovelock theory in various dimensions. This allows one to write down the black-hole solution which depends on many parameters (coupling constants in front of higher curvature terms) in a very compact analytic form, which depends only upon a few parameters of the parametrization. The approximate metric deviates from the exact (but extremely cumbersome) expressions by fractions of one percent even at the first order of the continued-fraction expansion, which is confirmed here by computation of observable quantities, such as quasinormal modes of the black hole.