Regular evaporating black holes with stable cores

Abstract

We reply to the "Comment" on "Regular evaporating black holes with stable cores" by R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio, and M. Visser. As a key result, we show that the regime of mass-inflation identified in the comment connects smoothly to the late-time attractors discovered in our works [A. Bonanno et. al., Regular black holes with stable cores, Phys. Rev. D 103, 124027 (2021) and Regular evaporating black holes with stable cores, Phys. Rev. D 107, 024005 (2023)]. Hence, the late-time stability of regular black holes is not affected by this intermediate phase.

Black Holes in Asymptotically Safe Gravity

“…Their importance lies in that (i) the cosmological constant, in non-unimodular settings, might re-introduce the curvature singularity-unless the dimensionless cosmological constant vanishes at high energies and critical exponents satisfy certain bounds [74,75], (ii) non-rotating black holes are unlikely configurations and, moreover, spin is decisive in establishing the shadow properties of black holes beyond general relativity [83][84][85], (iii) gravitational collapse renders singularity resolution less straightforward than in the static case, and it is likely that its endpoint be a black hole with an integrable singularity rather than a regular one [97][98][99][100][101][102][103][104][105]. In particular, this scenario might be desirable as it naturally avoids the potential perturbative instabilities characterizing regular black holes [64][65][66][67][68][69][70][71].…”

“…The antiscreening of gravity at high energies can in principle limit the increase rate of the mass function, and could at least weaken the singularity classically formed at the Cauchy horizon [48]. However, the question of mass inflation and inner horizon (in)stability is still under heated debate [64][65][66][67][68][69][70][71]. 5 Black hole temperature against the ADM mass m for classical (blu line) and RG-improved (green line) black holes.…”

“…Specifically, the singularity at r = 0 turns out to be gravitationally weak (or, integrable, according to Tipler classification [116]): curvature invariants diverge as r → 0 but the geodesic equation can be integrated, so that the spacetime is geodesically complete. The case of black holes with integrable singularities, as the one derived in [102] and further explored in [103,104], is particularly important, as it could provide a consistent alternative to regular black holes whose inner horizon is unstable [64][65][66][67][68][69][70][71].…”

Suppression of spacetime singularities in quantum gravity

“…There exist several indications that this is the case. In particular, regular black-hole spacetimes have been found in superrenormalizable infinite-derivative quantum gravity [97,103], non-local gravity [72,95,[104][105][106], asymptotically safe quantum gravity [29][30][31][32][33][34][35][36]107] and recent studies explicitly taking into account infinite towers of highercurvature corrections [108]. These findings contrast black-hole solutions in perturbatively renormalizable models, such as quadratic gravity where spacetime singularities persist [51,55].…”

Disentangling photon rings beyond General Relativity with future radio-telescope arrays

“…3 Regular black holes are usually understood as phenomenological models, but not yet as the ultimate and correct description of a fully consistent black-hole spacetime [118], due to the following reason: regular black holes contain inner horizons, which become Cauchy horizons if not disappearing in finite time due to evaporation or some other process. The spacetime region around inner horizons generically displays an exponential focusing of null rays unless the inner surface gravity vanishes [119,120], which results in an exponential mass inflation phase in which curvature invariants grow exponentially [121,122] (see also [123][124][125][126]). The endpoint of this dynamical evolution is unknown, and is a question to be addressed in specific dynamical frameworks leading to regular black hole solutions.…”