Global curvature control in a regular black hole with Minkowski core and inner-extremal horizon

Abstract

We construct a static, spherically symmetric regular black hole with a Minkowski core, a non-extremal outer horizon, and a degenerate inner horizon with vanishing surface gravity. The spacetime exhibits two main features. First, in the large-mass regime with $r_{+}=2M$, the maximal Kretschmann scalar becomes nearly independent of the ADM mass and is mainly controlled by the inner-horizon radius $r_{-}$, providing a simple sufficient condition for the curvature to remain sub-Planckian everywhere. Second, the effective cubic zero of the metric function replaces the standard exponential near-horizon amplification with power-law behavior. A massless scalar test field shows that the geometric blueshift factor grows as $v^{3/2}$. Then, we use the double-null shell and Ori models to examine the corresponding effective mass dynamics. the nonlinear shell-crossing contribution decays at late times, while the Ori evolution with a Price-law ingoing flux keeps the internal Misner-Sharp mass bounded. In both descriptions, the late-time mass approaches $r_{-}/2$. The same inner-horizon scale therefore controls the global curvature bound and the finite mass scale reached by the shell dynamics.

arXiv comment14pages, 5 figures. Accepted for publication in European Physical Journal C