Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles

Abstract

We study modifications of general relativity, GR, with nonlinear dispersion relations which can be geometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravitational Lagrange density functionals $f(\mathbf{R},\mathbf{T},F)$ with generalized/ modified scalar curvature $\mathbf{R}$, trace of matter field tensors $\mathbf{T}$ and modified Finsler like generating function $F$. In particular, there are defined extensions of GR with extra dimensional "velocity/ momentum" coordinates. For four dimensional models, we prove that it is possible to decouple and integrate in very general forms the gravitational fields for $f(\mathbf{R},\mathbf{T},F)$-modified gravity using nonholonomic 2+2 splitting and nonholonomic Finsler like variables $F$. We study the modified motion and Newtonian limits of massive test particles on nonlinear geodesics approximated with effective extra forces orthogonal to the four--velocity. We compute the constraints on the magnitude of extra-accelerations and analyze perihelion effects and possible cosmological implications of such theories. We also derive the extended Raychaudhuri equation in the framework of a tangent Lorentz bundle. Finally, we speculate on effective modelling of modified theories by generic off-diagonal configurations in Einstein and/or MGTs and Finsler gravity. We provide some examples for modified stationary (black) ellipsoid configurations and locally anisotropic solitonic backgrounds.

latex2e, 20 pages; version accepted to IJMPD; changed title and modifications following requests of referee

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Cited by in corpus (22)

• Finsler gravity action from variational completion
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Berwald spacetimes and very special relativity
• Schwarzschild-like solutions in Finsler-Randers gravity
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• On the non metrizability of Berwald Finsler spacetimes
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Applications of the Schwarzschild-Finsler-Randers model
• Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
• Randers pp-waves
• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• Gravitational Field on the Lorentz Tangent Bundle: Generalized Paths and Field Equations
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• A Cosmological Unicorn Solution to Finsler Gravity
• Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry
• 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
• Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
• On the significance of the stress-energy tensor in Finsler spacetimes
• Birkhoff Theorem for Berwald Finsler spacetimes
• Finslerian geometrodynamics