A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions

TL;DR

This paper develops a geometric method to construct exact off-diagonal solutions in modified f(R,T)-gravity coupled with Yang-Mills and Higgs fields, including black hole and solitonic configurations.

Contribution

It introduces a novel geometric technique for generating exact solutions in f(R,T) gravity with gauge fields, accommodating complex off-diagonal metrics and symmetries.

Findings

Constructed explicit off-diagonal solutions with Killing symmetries.

Derived solutions describing black hole, ellipsoid, and solitonic configurations.

Simplified solution generation for metrics with at least one Killing vector.

Abstract

We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.