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A common argument suggests that non-singular geometries may not describe black holes observed in nature since they are unstable due to a mass-inflation effect. We analyze the dynamics associated with spherically symmetric, regular black holes taking the full backreaction between the infalling matter and geometry into account. We identify the crucial features taming the growth of the mass function and a diminished curvature singularity at the Cauchy horizon and demonstrate that the regular black hole solutions proposed by Hayward and obtained from Asymptotic Safety satisfy these properties.
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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.
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.
In this work, we consider that in energy scales greater than the Planck energy, the geometry, fundamental physical constants, as charge, mass, speed of light and Newtonian constant of gravitation, and matter fields will depend on the scale. This type of theory is known as Rainbow Gravity. We coupled the nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function $M(r,epsilon)$, such that we may formulate new classes of spherically symmetric regular black hole solutions, where the curvature invariants are well-behaved in all spacetime. The main differences between the General Relativity and our results in the the Rainbow gravity are: a) The intensity of the electric field is inversely proportional to the energy scale. The higher the energy scale, the lower the electric field intensity; b) the region where the strong energy condition (SEC) is violated decrease as the energy scale increase. The higher the energy scale, closer to the radial coordinate origin SEC is violated.
Using the covariant phase space formalism, we compute the conserved charges for a solution, describing an accelerating and electrically charged Reissner-Nordstrom black hole. The metric is regular provided that the acceleration is driven by an external electric field, in spite of the usual string of the standard C-metric. The Smarr formula and the first law of black hole thermodynamics are fulfilled. The resulting mass has the same form of the Christodoulou-Ruffini mass formula. On the basis of these results, we can extrapolate the mass and thermodynamics of the rotating C-metric, which describes a Kerr-Newman-(A)dS black hole accelerated by a pulling string.
We elaborate on the role of higher-derivative curvature invariants as a quantum selection mechanism of regular spacetimes in the framework of the Lorentzian path integral approach to quantum gravity. We show that for a large class of black hole metrics prominently regular there are higher-derivative curvature invariants associated with a singular term in the action. Therefore, according to the finite action principle applied to a general higher-derivative gravity model, not only singular spacetimes but also some of the regular ones seem to not contribute to the path integral.
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