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

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--Nordström 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.

Figures (2)

• Figure 1: Colliding spherical thin null shells near the inner (Cauchy) horizon inside the black hole. The domain $T_-$ splits into four regions $A,B,C,$ and $D$, separated by null shells.
• Figure 2: The typical shape of functions $f(r)$ for regular black holes. The external horizon is located at $r_{\hbox{\scriptsize g}}$ and the internal one is at $r_*.$