Gravi-Weak Unification and the Black-Hole-Hedgehog's Solution with Magnetic Field Contribution

TL;DR

This paper explores black-hole-hedgehog solutions with magnetic fields within f(R)-gravity under the Gravi-Weak unification model, analyzing topological defects in a universe with two degenerate vacua and their stability.

Contribution

It introduces a novel black-hole-hedgehog solution as a topological defect in the false vacuum, including detailed metric and stability analysis within the Gravi-Weak unification framework.

Findings

Derived a black-hole-hedgehog solution with specific core mass and radius.

Estimated the horizon radius of the black-hole-hedgehog.

Confirmed the stability of the electroweak vacuum during phase transition.

Abstract

In the present paper, we investigated the gravitational black-hole-hedgehog's solution with magnetic field contribution in the framework of the f(R)--gravity described by the Gravi-Weak unification model. Assuming the Multiple Point Principle (MPP), we considered the existence of the two degenerate vacua of the Universe: the first Electroweak (EW) vacuum with $v_1 \approx 246$ GeV ("true vacuum"), and the second Planck scale ("false vacuum") with $v_2 \sim 10^{18}$ GeV. In these vacua, we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehog configurations as defects of the "false vacuum". We have obtained the solution which corresponds to a global monopole, that has been "swallowed" by the black-hole with core mass $M_{BH}\approx 3.65\times 10^{18}\,\, {\rm{GeV}}$ and radius $\delta \approx 6\cdot 10^{-21} {\rm{GeV}}^{-1}.$ We investigated the metric in the vicinity of the black-hole-hedgehog and estimated its horizon radius: $r_h\approx 1.14 \delta$. We have considered the phase transition from the "false vacuum" to the "true vacuum" and confirmed the stability of the EW--vacuum.