Charged black holes in quadratic gravity

TL;DR

This paper constructs iterative solutions for static, charged black holes in quadratic gravity, analyzing extremal cases and near-horizon geometries, and compares different boundary condition approaches.

Contribution

It provides explicit iterative solutions for charged black holes in quadratic gravity, including extremal cases and their near-horizon geometries, with analysis of different boundary conditions.

Findings

Extremal black hole horizon location is |e|.

Near-horizon geometry matches Bertotti-Robinson spacetime.

Solutions parametrized by charge and horizon location.

Abstract

Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. Obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit, the exact location of the (degenerate) event horizon is given by $\rp = |e|.$ Similarly to the classical Reissner-Nordstr\"om solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for the boundary conditions of second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed.