Regular black holes with sub-Planckian curvature

Abstract

We construct a sort of regular black holes with a sub-Planckian Kretschmann scalar curvature.The metric of this sort of regular black holes is characterized by an exponentially suppressing gravity potential as well as an asymptotically Minkowski core. In particular, with different choices of the potential form, they can reproduce the metric of Bardeen/Hayward/Frolov black hole at large scales. The heuristical derivation of this sort of black holes is performed based on the generalized uncertainty principle over curved spacetime which includes the effects of tidal force on any object with finite size which is bounded below by the minimal length.

The shadow of regular black holes with asymptotically Minkowski core

“…Such a discrepancy may be understood as the reflection of their different structure inside the horizon of black holes, where the former has a Minkowski core, while the latter has a de Sitter core. In particular, in [32] it is disclosed that for regular black hole with γ = 2/3 and n = 2, the position with the maximum of Kretschmann scalar curvature runs away from the core of the black hole, while for Bardeen black hole, the position of the maximal Kretschmann scalar curvature maintains at the center of the hole. In this sense, the regular black hole with γ = 2/3 and n = 2 may become more attractive to photons such that the silhouette of shadow is more deformed in comparison with that of Bardeen black hole.…”

“…In [32] we have proposed a new sort of regular spherically symmetric black holes with the following metric…”

“…Finally, the correspondence of such regular black holes to the ones with asymptotically de Sitter core has been pointed out in [32], where m(r) takes the form as…”

“…Taking the quantum effects of gravity into account, it is believed that these singularities could be removed or avoided. Before a well-defined theory of quantum gravity could be established, people have constructed various regular black holes without singularity at the phenomenological level [27][28][29][30][31][32][33]. These regular black hole models are characterized by a finite Kretschmann scalar curvature.…”

“…We organize the paper as follows. In next section we extend the regular black hole with spherical symmetry proposed in [32] to the rotating Kerr-like one, and then obtain the null geodesics with circular orbit near the horizon of black hole with the Hamilton-Jacobi formalism. In section three and four, we will investigate the shadow of regular black holes with (γ = 2/3, n = 2) and (γ = 1, n = 3), respectively, and compare them with the shadow of Bardeen and Hayward black holes with the same values of parameters.…”