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.

arXiv comment37 pages, IJGMMP style, a review of authors' contributions at conferences and seminars

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• f(R,T) gravity
• Superstring Cosmology
• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
• Solutions for f(R) gravity coupled with electromagnetic field
• Ellipsoidal, Cylindrical, Bipolar and Toroidal Wormholes in 5D Gravity
• Scalar Quarkonia at Finite Temperature
• Particle-like solutions to higher order curvature Einstein--Yang-Mills systems in d dimensions
• Investigation of heavy-heavy pseudoscalar mesons in thermal QCD Sum Rules
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations
• On General Solutions of Einstein Equations
• On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
• Decoupling of Field Equations in Einstein and Modified Gravity
• Cosmological monopoles and non-abelian black holes
• Covariant Renormalizable Anisotropic Theories and Off-Diagonal Einstein-Yang-Mills-Higgs Solutions
• On cosmological solutions in a spontaneously broken gauge theory
• Gravitational Flux Tubes

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• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in $R^2$ and Einstein Gravity Theories
• Effective Einstein Cosmological Spaces for Non-Minimal Modified Gravity
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• 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
• 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
• Gödel and Gödel-type solutions in the Palatini $f(R,T)$ gravity theory