# Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: analytical approximation

## TL;DR

This paper presents an analytical approximation of a non-Schwarzschild black hole metric in higher derivative gravity, enabling easier analysis of black hole properties within string-inspired theories.

## Contribution

The authors derive a rapidly converging analytical form of a numerically obtained black hole metric in higher derivative gravity, facilitating comprehensive studies of its physical characteristics.

## Key findings

- Analytical metric accurately represents the numerical solution across all space.
- Enables detailed analysis of black hole thermodynamics and stability.
- Simplifies the study of black hole perturbations and quasinormal modes.

## Abstract

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in the Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.