Topological black holes in higher derivative gravity

Alena Pravdová; Vojtěch Pravda; Marcello Ortaggio

doi:10.1140/epjc/s10052-023-11338-9

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 180
https://doi.org/10.1140/epjc/s10052-023-11338-9

Regular Article - Theoretical Physics

Topological black holes in higher derivative gravity

Alena Pravdová^a, Vojtěch Pravda and Marcello Ortaggio

Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Prague 1, Czech Republic

^a pravdova@math.cas.cz

Received: 30 January 2023
Accepted: 13 February 2023
Published online: 25 February 2023

Abstract

We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants – the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein’s gravity, such black holes require a negative cosmological constant $Λ$ $\Lambda$ , in quadratic gravity they can exist for any sign of $Λ$ $\Lambda$ and also for $Λ = 0$ $\Lambda =0$ . Different branches of Schwarzschild–Bach–(A)dS or purely Bachian black holes are identified which admit distinct Einstein limits. Depending on the curvature of the transverse space and the value of $Λ$ $\Lambda$ , these Einstein limits result in (A)dS–Schwarzschild spacetimes with a transverse space of arbitrary curvature (such as black holes and naked singularities) or in Kundt metrics of the (anti-)Nariai type (i.e., dS $_{2} \times$ $_2\times$ S $^{2}$ $$^2$$ , AdS $_{2} \times$ $_2\times$ H $^{2}$ $$^2$$ , and flat spacetime). In the special case of toroidal black holes with $Λ = 0$ $\Lambda =0$ , we also discuss how the Bach parameter needs to be fine-tuned to ensure that the metric does not blow up near infinity and instead matches asymptotically a Ricci-flat solution.

© The Author(s) 2023

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