Slowly rotating solution of quadratic gravity: An analytical approximation method

Abstract

As we know, it is a nontrivial task to obtain analytical solutions for various gravitational theories. In this work, we obtain an analytical approximate rotating black hole solution for quadratic gravity (QG). To get a complete solution, we construct near-horizon and asymptotic solutions and then use these limited cases to obtain an approximate analytic solution through a continued fraction method. By checking the first law of thermodynamics and the Smarr formula, we studied the thermodynamics of the black hole solution. Finally, we investigate various physical properties of the solution including its photon sphere, and shadow.