Regular black holes inspired by quasi-topological gravity

Abstract

Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions describing regular black holes. Its reduced action depends on a function of one of the basic curvature invariants of the corresponding metric. In this paper we study a generalization of this model to the case when this function depends on all the basic curvature invariants. We show that the metrics which are solutions of such a model possess a universal scaling property. We demonstrate that there exists a special class of such models for which the ``master" equation for a basic curvature invariant is a linear second order ordinary differential equation. We specify a domain in the space of parameters of the model for which the corresponding solutions describe regular static spherically symmetric black holes and study their properties.

18 pages, 10 figures, a new section added, references added

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• Long-lived quasinormal modes, shadows and particle motion in four-dimensional quasi-topological gravity
• Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
• Regular black holes from pure gravity in four dimensions
• Scalar Quasinormal Modes of Rotating Regular Black Holes
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities
• Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities
• Shadows of a Non-Commutative Black Hole under the Influence of a Magnetized Plasma
• Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections