Weak Gravitational Field in Finsler-Randers Space and Raychaudhuri Equation

Abstract

The linearized form of the metric of a Finsler - Randers space is studied in relation to the equations of motion, the deviation of geodesics and the generalized Raychaudhuri equation are given for a weak gravitational field. This equation is also derived in the framework of a tangent bundle. By using Cartan or Berwald-like connections we get some types "gravito - electromagnetic" curvature. In addition we investigate the conditions under which a definite Lagrangian in a Randers space leads to Einstein field equations under the presence of electromagnetic field. Finally, some applications of the weak field in a generalized Finsler spacetime for gravitational waves are given.

22 pages, matches version published in GERG

References in corpus (4)

• Riemann-Finsler geometry and Lorentz-violating kinematics
• Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
• Raychaudhuri's equation and aspects of relativistic charged collapse
• Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

Cited by in corpus (26)

• Bipartite Riemann-Finsler geometry and Lorentz violation
• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Classical-physics applications for Finsler $b$ space
• Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model
• Covariant kinematics and gravitational bounce in Finsler space-times
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Finsler pp-waves
• Dynamics in Varying vacuum Finsler-Randers Cosmology
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles
• Schwarzschild-like solutions in Finsler-Randers gravity
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• The peculiar Raychaudhuri equation
• Applications of the Schwarzschild-Finsler-Randers model
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Cosmic magnetization in curved and Lorentz violating space-times
• Relativistic Finsler geometry
• Gravitational Field on the Lorentz Tangent Bundle: Generalized Paths and Field Equations
• The Raychaudhuri equation for spinning test particles
• Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds
• Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
• Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures
• Raychaudhuri equations, Tidal forces and Weak field Limit in Schwarzshild-Finsler-Randers spacetime
• Covariant kinematics of light in media and a generalized Raychaudhuri equation
• Focusing of world-lines in Weyl gravity
• Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications