Regular Black Holes from Collapsing Dust in a Dark Energy Background

Abstract

The central singularity in gravitational collapse represents a fundamental breakdown of classical general relativity, yet its resolution remains an open challenge. While conventional regular black hole models invoke exotic matter or nonlinear electrodynamics, the physical origin of such regularization mechanisms remains obscure. In this work, we demonstrate that a radially varying interaction between dust and dark energy can naturally resolve the central singularity. We systematically investigate three cases: no interaction, constant interaction, and radially varying interaction. Only when the interaction grows sufficiently toward the center can the divergent behavior of the density and the central mass contribution simultaneously be eliminated near the center. This yields a mass function scales as $M \sim \chi^3$, a finite Kretschmann scalar ($\lim_{\chi \to 0} K < \infty$), and a de Sitter-like core for the physical regime $w \leq -1$ (with $w=-1$ corresponding to pure de Sitter core). At the center, the resulting configuration satisfies the null, weak, and dominant energy conditions, while the strong energy condition is violated. Unlike charge-based models, our interaction parameter $\alpha(t)$ stabilizes at a non-zero value after the collapse, allowing the regular core to persist in the late-time configuration. This provides a physically motivated alternative to conventional regular black hole models, grounded in the modern cosmological understanding of dark energy rather than exotic fields or charges.