Regular Black Holes in Quasitopological Gravity: Null Shells and Mass Inflation

TL;DR

This paper studies mass inflation inside regular black holes in quasitopological gravity, showing it occurs only very close to the horizon at scales much smaller than the fundamental length, unlike in classical black holes.

Contribution

It demonstrates that mass inflation in regular quasitopological black holes requires shell collision extremely close to the horizon, differing from classical black hole models.

Findings

Mass inflation occurs only near the horizon at distances much smaller than the fundamental scale.

Significant mass inflation requires shell intersection at radii very close to the horizon.

The scale of shell intersection depends on the black hole parameters and the QTG model.

Abstract

We investigate the phenomenon of mass inflation in the interior of regular black holes arising in quasitopological gravity (QTG). These geometries are characterized by a bounded curvature core and the presence of an inner (Cauchy) horizon located near the fundamental scale $\ell$. To examine whether mass inflation persists in this setting, we model the interaction of ingoing and outgoing perturbations by considering the collision of two spherical null shells inside the black hole. Using the Dray-'t\,Hooft-Barrabes-Israel junction condition, we derive conditions under which the metric function and curvature invariants may experience significant amplification near the inner horizon. Our analysis shows that, unlike in classical Reissner--Nordstr\"om or Kerr geometries, significant mass inflation requires shell intersection at radii very close to the horizon, with radial separations from it of the order $r-r_* \lesssim \ell \big(\ell/r_g\big)^{2n(D-3)}$, where $r_g$ is the gravitational radius of the black hole, $D$ is the number of spacetime dimensions and $n\ge 1$ is a parameter depending on a concrete QTG model. For macroscopic black holes with $r_g\gg \ell$ this distance is much smaller than the fundamental scale $\ell$. We discuss possible consequences of this effect.