Exact black holes in quadratic gravity with any cosmological constant

TL;DR

This paper introduces a new class of explicit black hole solutions in quadratic gravity with a cosmological constant, characterized by constant scalar curvature and a three-parameter family, including their horizons, thermodynamics, and tidal effects.

Contribution

It provides the first explicit solutions for black holes in quadratic gravity with a cosmological constant, derived under constant scalar curvature and analyzed through a simplified autonomous system.

Findings

Existence of black-hole and cosmological horizons for positive cosmological constant.

Explicit power series solutions for the metric functions.

Analysis of tidal effects and thermodynamic properties.

Abstract

We present a new explicit class of black holes in general quadratic gravity with a cosmological constant. These spherically symmetric Schwarzschild-Bach-(anti-)de Sitter geometries (Schwa-Bach-(A)dS), derived under the assumption of constant scalar curvature, form a three-parameter family determined by the black-hole horizon position, the value of Bach invariant on the horizon, and the cosmological constant. Using a conformal to Kundt metric ansatz, the fourth-order field equations simplify to a compact autonomous system. Its solutions are found as power series, enabling us to directly set the Bach parameter and/or cosmological constant equal to zero. To interpret these spacetimes, we analyse the metric functions. In particular, we demonstrate that for a certain range of positive cosmological constant there are both black-hole and cosmological horizons, with a static region between them. The tidal effects on free test particles and basic thermodynamic quantities are also determined.