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

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.

37 pages, IJGMMP style, a review of authors' contributions at conferences and seminars

References in corpus (4)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Cosmological monopoles and non-abelian black holes

Cited by in corpus (3)

• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Gödel and Gödel-type solutions in the Palatini $f(R,T)$ gravity theory
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories