Exact solution of vacuum field equation in Finsler spacetime

Abstract

We suggest that the vacuum field equation in Finsler spacetime is equivalent to vanishing of Ricci scalar. Schwarzschild metric can be deduced from a solution of our field equation if the spacetime preserve spherical symmetry. Supposing spacetime to preserve the symmetry of "Finslerian sphere", we find a non-Riemannian exact solution of the Finslerian vacuum field equation. The solution is similar to the Schwarzschild metric. It reduces to Schwarzschild metric while the Finslerian parameter $\epsilon$ vanishes. It is proved that the Finslerian covariant derivative of the geometrical part of the gravitational field equation is conserved. The interior solution is also given. We get solutions of geodesic equation in such a Schwarzschild-like spacetime, and show that the geodesic equation returns to the counterpart in Newton's gravity at weak field approximation. The celestial observations give constraint on the Finslerian parameter $\epsilon <10^{-4}$. And the recent Michelson-Morley experiment requires $\epsilon <10^{-16}$. The counterpart of Birkhoff's theorem exist in Finslerian vacuum. It shows that the Finslerian gravitational field with the symmetry of "Finslerian sphere" in vacuum must be static.

25 pages

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Cited by in corpus (39)

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• Cosmological evolution and dark energy in osculating Barthel-Randers geometry
• Berwald spacetimes and very special relativity
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Relativistic kinetic gases as direct sources of gravity
• Standard static Finsler spacetimes
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• Dark energy and accelerating cosmological evolution from osculating Barthel-Kropina geometry
• A unified description for dipoles of the fine-structure constant and SnIa Hubble diagram in Finslerian universe
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• Anisotropic strange star in Finsler geometry
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• A tomographic test of cosmological principle using the JLA compilation of type Ia supernovae
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• Affine sphere relativity
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• Primordial power spectrum of tensor perturbations in Finsler spacetime
• Affine sphere spacetimes which satisfy the relativity principle
• Black Ring and Kerr Ellipsoid - Solitonic Configurations in Modified Finsler Gravity
• Finslerian dipolar modulation of the CMB power spectra at scales $2<l<600$
• Ricci flat Finsler metrics by warped product
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• Noncommutative black hole in the Finslerian spacetime
• Anisotropic power spectrum and the observed low-l power in PLANCK CMB data
• Spatial and temporal variations of the fine-structure constant in the Finslerian universe
• On the significance of the stress-energy tensor in Finsler spacetimes
• Cosmological solutions and finite time singularities in Finslerian geometry
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Remark on Remnant and Residue Entropy with GUP
• Particle motion and scattering in Finslerian Schwarzschild metric
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