Related papers: Redshift in Finsler spacetimes
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. We present the arrival time delay of astroparticles subject to Lorentz violation in the…
This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper (Class. Quantum Grav. \textbf{35}(16) (2018), 165003). The spacetime at issue is topologically trivial, free of…
We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that…
We calculate the low red-shift Taylor expansion for the luminosity distance for an observer at the center of a spherically symmetric matter inhomogeneity with a non vanishing cosmological constant. We then test the accuracy of the formulas…
It is shown that if a variable cosmological term in the present Universe is described by a scalar field with minimal coupling to gravity and with some phenomenological self-interaction potential $V(\varphi)$, then this potential can be…
Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…
We present a set of localized states for an even number of Dirac fermions under Einsteinian gravity that have an infinite central redshift. Near the center of the localized state the components of the Dirac spinor and the spacetime metric…
The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The…
In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the…
This PhD dissertation covers a range of topics in Finsler geometry and Finsler gravity, most notably: (i) the characterization of Berwald spaces, (ii) pseudo-Riemann (non-)metrizability of Berwald spaces, (iii) $(\alpha,\beta)$-metrics,…
We find the generalization of Einstein equations to Finsler spaces by variational means and, based on the invariance of the Finslerian Hilbert action to infinitesimal transformations, we find the analogue of the energy- momentum…
The Finslerian extension of the Euclidean metric is proposed and studied under rigorous conditions that the associated indicatrix is regular and convex. The relativistic pseudo-Euclidean metric is extended, too. The extensions show distinct…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…
Here, an axiom of spheres in Finsler geometry is proposed and it is proved that if a Finslerian manifold satisfies the axiom of spheres then it is of constant flag curvature.
We study the dynamical evolution of two quantum clocks interacting with a relativistic gravitational potential. We find a time dilation effect for the clocks in agreement with the gravitational time dilation as obtained from the…
We find exact Fermi coordinates for timelike geodesic observers for a class of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the constant density interior Schwarzschild spacetime with positive, zero, and negative…
We show that Rindler horizons are entropic screens and gravity is an entropic force in Rindler space by deriving the Verlinde entropy formula from the focusing of light due to a mass close to the horizon. Consequently, gravity is also…
Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. Because physicists need to use pseudo-Finsler structures to describe propagation}of signals, there will be nonzero null…
We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.
The method of simple straightforward calculation of the curvature tensor of the Finsleroid--regular space is indicated. The Schwarzschild metric which underlines the gravitational field produced by static spherical-symmetric body is shown…