Dymnikova GUP-corrected black holes

TL;DR

This paper investigates how GUP effects influence Dymnikova regular black holes, revealing that they remain singularity-free with modified internal structures and altered energy condition violations at quantum scales.

Contribution

It provides an analytical and numerical analysis of GUP-corrected Dymnikova black holes, showing the persistence of regularity and new internal features like wormholes.

Findings

Black holes remain singularity-free under GUP corrections.

A wormhole can form inside the de Sitter core.

Energy condition violations are suppressed at Planckian scales.

Abstract

We consider the impact of Generalized Uncertainty Principle (GUP) effects on the Dymnikova regular black hole. The minimum length scale introduced by the GUP modifies the energy density associated with the gravitational source, referred to as the Dymnikova vacuum, based on its analogy with the gravitational counterpart of the Schwinger effect. We present an approximated analytical solution (together with exact numerical results for comparison) that encompasses a wide range of black hole sizes, spanning from microscopic (Planckian and sub-Planckian) to macroscopic scales, whose properties crucially depend on the ratio between the de Sitter core radius and the GUP scale. The emergence of a wormhole inside de Sitter core in the innermost region of the object is one of the most relevant features of this family of solutions. Our findings demonstrate that these solutions remain singularity free, confirming the robustness of the Dymnikova regular black hole under GUP corrections. Regarding energy conditions, we find that the violation of the strong, weak, and null energy conditions which is characteristic of the pure Dymnikova case does not occur at Planckian scales in the GUP corrected solution. This contrast suggests a departure from conventional expectations and highlights the influence of quantum corrections and the GUP in modifying the energy conditions near the Planck scale.