10 research outputs found
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-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 . 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 . 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
(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)