Schwarzschild-like solutions in Finsler–Randers gravity

Abstract

In this work, we extend for the first time the spherically symmetric Schwarzschild and Schwarzschild–De Sitter solutions with a Finsler–Randers-type perturbation which is generated by a covector $$A_\gamma $$ A γ . This gives a locally anisotropic character to the metric and induces a deviation from the Riemannian models of gravity. A natural framework for this study is the Lorentz tangent bundle of a spacetime manifold. We apply the generalized field equations to the perturbed metric and derive the dynamics for the covector $$A_\gamma $$ A γ . Finally, we find the timelike, spacelike and null paths on the Schwarzschild–Randers spacetime, we solve the timelike ones numerically and we compare them with the classic geodesics of general relativity. The obtained solutions are new and they enrich the corresponding literature.

Applications of the Schwarzschild–Finsler–Randers model

“…The solution of these equations for this metric is presented at the end of the section. An extended study of this model can be found in [40,44].…”

“…In this work, we will follow the model presented in [40]. The metric g μν is the classic Schwarzschild one:…”

“…Solving the above equations to first order in A γ (x) in vacuum (T μν = Y αβ = Z κ α = 0), we get [40]:…”

“…More investigations about this model can be found in the following articles [6,15,30,[53][54][55][56][57][58][59][60]. By using a Schwarzschild metric in (1), we obtain a Schwarzschild-Randers spacetime [40].…”

“…In this article, we investigate further properties and applications of our previous work of the SFR model which generalizes the classical Schwarzschild spacetime by introducing a timelike covector A γ in the metric structure[40]. This covector is specified by the solution of the generalized Einstein equations of the SFR model.…”