More on Analytically Approximate Solution to Quadratic Gravity

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.