More on Analytically Approximate Solution to Quadratic Gravity

TL;DR

This paper develops an analytical approximation method for static, spherically symmetric black hole solutions in quadratic gravity, compares these with numerical solutions, and analyzes their stability.

Contribution

It introduces a continued fraction expansion approach to approximate black hole solutions in Einstein-Weyl squared gravity and explores their properties and stability.

Findings

Four branches of black hole solutions with positive ADM mass identified.

A non-Schwarzschild solution emerges at specific integration constants.

Thermodynamic and dynamical stability of solutions analyzed.

Abstract

In this work, we obtain the analytically approximation of static, spherically symmetric black hole solutions to Einstein$-$Weyl squared gravity by using the continued fraction expansion method. The black hole solutions are found for various relations between near horizon parameters with positive Weyl's coupling constant $\alpha$. Black hole solutions associated with different near-horizon constants are compared with the numerical ones. We obtain four branches of the black hole solutions with positive Arnowitt-Deser-Misner (ADM) mass. A non-Schwarzschild solution appears when the integration constant reaches a certain value for arbitrary values of the coupling constant {$\alpha$}. In addition, we study the thermodynamic and dynamical stability of the black hole solutions by considering thermodynamic quantities and the quasinormal frequencies.