Schwarzschild-like solutions in Finsler-Randers gravity

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 $A_\gamma$. 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 $A_\gamma$. 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.Comment: 13 pages, 2 figures, to be published in EPJ

Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle

In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors. We will examine the dynamical analysis of geodesics which provides the derivation of the energy and the angular momentum of a particle moving along a geodesic of SFR spacetime. This study allows us to compare our model with the corresponding of general relativity (GR). In addition, the effective potential of SFR model is examined and it is compared with the effective potential of GR. The phase portraits generated by these effective potentials are also compared. Finally, we deal with the derivation of the deflection angle of the SFR spacetime and we find that there is a small perturbation from the deflection angle of GR. It comes from the anisotropic metric structure of the model and especially from a Randers term which provides a small deviation from GR

Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle

In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis et al. in Eur Phys J C 81(11):990, 2021). We will examine the dynamical analysis of geodesics which provides the derivation of the energy and the angular momentum of a particle moving along a geodesic of SFR spacetime. This study allows us to compare our model with the corresponding of general relativity (GR). In addition, the effective potential of SFR model is examined and it is compared with the effective potential of GR. The phase portraits generated by these effective potentials are also compared. Finally we deal with the derivation of the deflection angle of the SFR spacetime and we find that there is a small perturbation from the deflection angle of GR. We also derive an interesting relation between the deflection angles of SFR model and the corresponding result in the work of Shapiro et al (Phys Rev Lett 92(12):121101, 2004). These small differences are attributed to the anisotropic metric structure of the model and especially to a Randers term which provides a small deviation from the GR.Comment: 21 pages, 5 figure

Gravitational field on the Lorentz tangent bundle: generalized paths and field equations

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. © 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature

Applications of the Schwarzschild–Finsler–Randers model

In this article, we study further applications of the Schwarzschild–Finsler–Randers (SFR) model which was introduced in a previous work Triantafyllopoulos et al. (Eur Phys J C 80(12):1200, 2020). In this model, we investigate curvatures and the generalized Kretschmann invariant which plays a crucial role for singularities. In addition, the derived path equations are used for the gravitational redshift of the SFR-model and these are compared with the GR model. Finally, we get some results for different values of parameters of the generalized photonsphere of the SFR-model and we find small deviations from the classical results of general relativity (GR) which may be ought to the possible Lorentz violation effects

Schwarzschild-like solutions in Finsler–Randers gravity

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 Aγ. 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 Aγ. 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. © 2020, The Author(s)

Finsler–Randers–Sasaki gravity and cosmology

Abstract We present for the first time a Friedmann-like construction in the framework of an osculating Finsler–Randers–Sasaki (F–R–S) geometry. In particular, we consider a vector field in the metric on a Lorentz tangent bundle, and thus the curvatures of horizontal and vertical spaces, as well as the extra contributions of torsion and non-linear connection, provide an intrinsic richer geometrical structure, with additional degrees of freedom, that lead to extra terms in the field equations. Applying these modified field equations at a cosmological setup we extract the generalized Friedmann equations for the horizontal and vertical space, showing that we obtain an effective dark energy sector arising from the richer underlying structure of the tangent bundle. Additionally, as it is common in Finsler-like constructions, we obtain an effective interaction between matter and geometry. Finally, we consider a specific model and we show that it can describe the sequence of matter and dark-energy epochs, and that the dark-energy equation of state can lie in the quintessence or phantom regimes, or cross the phantom divide