[Paper Review] Comment on "Regular evaporating black holes with stable cores"

Raúl Carballo-Rubio, Francesco Di Filippo+3 more|arXiv (Cornell University)|Dec 14, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper challenges recent claims that Hawking radiation stabilizes regular black holes by demonstrating that mass inflation instability persists due to unphysical numerical approximations in prior analyses. The authors show that the apparent finite mass growth in those studies results from using an ill-chosen variable ($m_+$) that diverges prematurely, invalidating their conclusions despite the model's physical breakdown under backreaction.

ABSTRACT

Regular black holes are generically unstable because of the classical phenomenon that goes by the name of "mass inflation" which destabilizes the inner horizon. In a recent article, [Phys.Rev.D~107~(2023)~2,~024005], it is argued that semiclassical effects due to Hawking radiation can cure this instability, and some concerns are raised against the validity of previous analyses showing its existence in the first place. In this short comment, we explain our reservations regarding these recent claims, and reiterate the relevance of the mass inflation instability for regular black holes of astrophysical interest.

Motivation & Objective

• To challenge recent claims that Hawking radiation stabilizes regular black holes with stable cores.
• To demonstrate that the apparent resolution of mass inflation instability in recent works stems from incomplete numerical integration using a non-physical variable.
• To reiterate the physical relevance of mass inflation in astrophysically relevant regular black hole models.
• To clarify the separation of timescales between ringdown, Price-law decay, and backreaction from Hawking radiation.
• To emphasize that only models accounting for backreaction can yield physically meaningful conclusions about the end state of regular black holes.

Proposed method

• Adopts the modified Ori model to analyze perturbations in a regular black hole spacetime with two horizons.
• Uses the Misner–Sharp quasi-local mass $ M_{ ext{MS}} $ as the primary physical variable to track energy growth, avoiding unphysical divergences.
• Performs numerical integration of the asymptotic mass $ m_+ $ and Kretschmann scalar $ K $ to track curvature growth and identify instability onset.
• Compares results with incomplete numerical analyses (e.g., Fig. 7 of Bonanno & Saueressig 2022) to expose premature truncation due to $ m_+ $ divergence.
• Analyzes the Hayward regular black hole metric with $ M_{ ext{MS}}(v,r) = \frac{m_{\pm} r^3}{r^3 + 2m_{\pm} \ell^2} $, where $ \ell $ is the regularization scale.
• Highlights that the Kretschmann scalar $ K $, which measures curvature, exhibits exponential-to-polynomial growth signaling the onset of backreaction.

Experimental results

Research questions

• RQ1 Can Hawking radiation truly stabilize regular black holes with non-extremal inner horizons?
• RQ2 Why do recent numerical studies report finite mass growth in regular black holes, contradicting established mass inflation results?
• RQ3 What is the physical significance of the divergence in the asymptotic mass $ m_+ $, and why does it invalidate numerical integration in that variable?
• RQ4 At what point does the linear approximation break down due to backreaction in regular black hole models?
• RQ5 What are the physically viable end states of regular black holes after mass inflation and backreaction?

Key findings

• The apparent finite mass growth reported in Bonanno & Saueressig (2022) is an artifact of using $ m_+ $ as the integration variable, which diverges at finite $ v $, halting the simulation prematurely.
• The Kretschmann scalar $ K $ exhibits exponential-to-polynomial growth, signaling the onset of significant backreaction, which invalidates the linear model before $ m_+ $ diverges.
• The numerical integration must be performed in terms of physically meaningful variables like the Misner–Sharp mass or curvature invariants, not $ m_+ $, which lacks clear physical interpretation.
• The exponential mass inflation instability persists regardless of background geometry, as shown in Carballo-Rubio et al. (2021), and is not cured by Hawking radiation.
• The model breaks down under backreaction long before $ m_+ $ diverges, meaning the linear approximation is unphysical beyond this point.
• The results confirm that regular black holes with non-extremal inner horizons are generically unstable, and their end states must be studied via full dynamical equations, not linearized models.