Related papers: Finsleroid-regular space: curvature tensor, contin…
In this paper we analyze the spacetime geometry due to a Schwarzschild object having uniform accelerated motion. In the beginning, we investigate the gravitational field due to a uniformly moving Schwarzschild object and obtain the…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
We compute the gravitational birefringence of light as it undergoes gravitational lensing. To this end we re-derive the Souriau-Saturnini equations in the Schwarzschild metric and solve them numerically and perturbatively. Our main result…
In this paper, we give the general form of spherically symmetric Finsler metrics in $R^n$ and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The…
The curvature tensor and the scalar curvature are computed in the space of positive definite real matrices endowed by the Kubo-Mori inner product as a Riemannian metric.
The renormalized expectation value of the stress energy tensor of the conformally invariant massless fields in the Unruh state in the Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in…
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…
We have obtained Finslerian Ressiner-Nordstrom solution where it is asymptotic to a Finsler spacetime with constant flag curvature while $r\rightarrow\infty$. The covariant derivative of modified Einstein tensor in Finslerian gravitational…
This article explores wormhole solutions within the framework of Finsler geometry and the modified gravity theory. Modifications in gravitational theories, such as $f(\mathcal{R}, \mathcal{T})$ gravity, propose alternatives that potentially…
In this article, we study the form of deviation of geodesics (tidal forces) and Raychaudhuri equation in a Schwarzshild-Finsler-Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by considering…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the…
In Schwarzschild spacetime the value $r=3m$ of the radius coordinate is characterized by three different properties: (a) there is a ``light sphere'', (b) there is ``centrifugal force reversal'', (c) it is the upper limiting radius for a…
We consider geodesics of massive and massless test particles in the gravitational field of a static and axisymmetric compact object described by the quadrupolar metric ($q$-metric), which is the simplest generalization of the Schwarzschild…
Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be…
We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds). There are analyzed alternatives to Einstein gravity (including…
Using distributional techniques we calculate the energy--momentum tensor of the Schwarzschild geometry. It turns out to be a well--defined tensor--distribution concentrated on the $r=0$ region which is usually excluded from space--time.…
We study Weitzenb\"ock's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenb\"ock's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions…
Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest…