Abstract
Standard models of “regular black holes” typically have asymptotically de Sitter regions at their cores. Herein, we shall consider novel “hollow” regular black holes, those with asymptotically Minkowski cores. The reason for doing so is twofold: First, these models greatly simplify the physics in the deep core, and second, one can trade off rather messy cubic and quartic polynomial equations for somewhat more elegant special functions such as exponentials and the increasingly important Lambert W function. While these “hollow” regular black holes share many features with the Bardeen/Hayward/Frolov regular black holes, there are also significant differences.
Highlights
It is well established that all static spherically symmetric spacetimes have a line element which can, without loss of generality, be represented in the following form [1,2]: ds = −e −2Φ(r ) 2m(r ) 1− r dt2 + dr2 + r2 dΩ22 . (1)Here, Φ(r ) and m(r ) are a priori arbitrary functions of r
The geometry is certainly modeling a black hole region of some description; it remains to demonstrate that the spacetime is gravitationally nonsingular in order to show this is a regular black hole in the sense pioneered by Bardeen [3]
We examine the non-zero components of the curvature tensors, as well as the curvature invariants, to show that, for a ∈ 0, 2m e, this metric does model a regular black hole geometry
Summary
Presented is a new and rather different form of the metric tensor, which is still a regular black hole in the sense of exhibiting everywhere finite curvature (as originally pioneered by Bardeen [3], see discussion below) but with an asymptotically Minkowski core (the energy density and associated pressures asymptote to zero). We may make this physical difference mathematically explicit by examining the required conditions on the two functions Φ(r ) and m(r ) appearing in the metric (1):. The overall framework these authors are working with differs significantly from our own
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