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 parametrized by the integration constants and the coupling constant 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 of a test scalar field.