(Anti-) de Sitter Electrically Charged Black Hole Solutions in Higher-Derivative Gravity

TL;DR

This paper explores static electrically charged black hole solutions with a cosmological constant in higher-derivative gravity, revealing both Schwarzschild and non-Schwarzschild (Anti-) de Sitter solutions through analytical and numerical methods.

Contribution

It introduces new non-Schwarzschild (Anti-) de Sitter black hole solutions in higher-derivative gravity, expanding understanding beyond classical solutions.

Findings

Existence of two distinct classes of asymptotically (Anti-) de Sitter black holes.

Reduction of one class to Schwarzschild (Anti-) de Sitter solutions in the uncharged case.

Identification of a second, intrinsically different class of solutions.

Abstract

In this paper, static electrically charged black hole solutions with cosmological constant are investigated in an Einstein-Hilbert theory of gravity with additional quadratic curvature terms. Beside the analytic Schwarzschild (Anti-) de Sitter solutions, non-Schwarzschild (Anti-) de Sitter solutions are also obtained numerically by employing the shooting method. The results show that there exist two groups of asymptotically (Anti-) de Sitter spacetimes for both charged and uncharged black holes. In particular, it was found that for uncharged black holes the first group can be reduced to the Schwarzschild (Anti-) de Sitter solution, while the second group is intrinsically different from a Schwarzschild (Anti-) de Sitter solution even when the charge and the cosmological constant become zero.