Gravitational Field on the Lorentz Tangent Bundle: Generalized Paths and Field Equations

Abstract

We investigate the dynamics of gravitational field and particles in a generalized framework of a Lorentz tangent bundle. By variating an appropriate action for each case, we obtain generalized forms of paths and generalized field equations for a Sasaki type metric. We show that Stokes theorem is modified with respect to general relativity due to local anisotropy and the presence of a nonlinear connection which induces an adapted basis in our space.

arXiv comment13 pages. arXiv admin note: text overlap with arXiv:2006.05913

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Cited by in corpus (10)

• Backgrounds in gravitational effective field theory
• Searches for beyond-Riemann gravity
• Schwarzschild-like solutions in Finsler-Randers gravity
• Finsler-Randers-Sasaki gravity and cosmology
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Applications of the Schwarzschild-Finsler-Randers model
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• Cosmological Landsberg Finsler spacetimes
• Raychaudhuri equations, Tidal forces and Weak field Limit in Schwarzshild-Finsler-Randers spacetime
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations