Quest for realistic non-singular black-hole geometries: Regular-center type

Abstract

We propose seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts. In general relativity, all such non-singular black holes are non-generic with a certain matter field including a class of nonlinear electromagnetic fields. According to a criterion that the effective energy-momentum tensor should satisfy all the standard energy conditions in asymptotically flat regions, the well-known Bardeen and Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang black holes respect the dominant energy condition everywhere. Although the rotating Fan-Wang black hole contains a curvature singularity, the rotating Dymnikova black hole is free from scalar polynomial curvature singularities and closed timelike curves. In addition, the dominant energy condition is respected on and outside the event horizons in the latter case. The absence of parallelly propagated curvature singularities remains an open question.

Black holes and their horizons in semiclassical and modified theories of gravity

“…186,187 Mass inflation has important consequences for RBH models. 128 Static RBHs have a causal structure that is similar to the Reissner-Nordström spacetime (Fig. 6(b) represents the extension of the Hayward model).…”

“…Indeed, many models of static black holes with 100,123,124 and without [125][126][127][128][129][130] a singularity have finite values of energy density −T t t =: ρ and pressure T r r =: p at the Schwarzschild radius r g . With respect to the invariants of Eq.…”

“…One of the simplest dynamical models of a RBH 40,126,128,147 is modification of the metric of Eq. ( 46) by adding the dependence of the mass parameter on the advanced time,…”

Charged BTZ-type solutions in Eddington-inspired Born-Infeld gravity

“…where from now on tildes over covariant derivatives imply that they are defined with respect to the tilded connection as defined in (6). From (7), it is straightforward to write the tilded connection in terms of the auxiliary metric to finally solve the connection field equation as follows…”

“…Such a state has not event horizon covering it but curvature scalars are everywhere finite, rendering it as a kind of regular naked object. This finding sparked the investigation of smoothing out black hole singularities by replacing the innermost region by de Sitter cores [3][4][5][6], the role of the BTZ solution within the AdS/CFT correspondence [7], or the analysis of its quasi-normal modes [8]. Moreover, the BTZ solution has been extended to include an electric charge [9,10] and further generalized to non-linear matter fields [11][12][13] and to the quantum realm [14].…”