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Due to the accuracy now reached by space geodetic techniques, and also considering some modelisations, the temporal variations of some Earth Gravity Field coefficients can be determined. They are due to Earth oceanic and solid tides, as…
We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature $\smash{\mathrm{Ric}_N}$ is bounded from below by a real number $K$ in every timelike direction satisfies the timelike…
We introduce a new class of $(\alpha,\beta)$-type exact solutions in Finsler gravity closely related to the well-known pp-waves in general relativity. Our class contains most of the exact solutions currently known in the literature as…
We use a specific geometric method to determine speed limits to the implementation of quantum gates in controlled quantum systems that have a specific class of constrained control functions. We achieve this by applying a recent theorem of…
The gravitational time advancement is a natural but a consequence of curve space-time geometry. In the present work the expressions of gravitational time advancement have been obtained for geodesic motions. The situation when the distance…
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of…
The geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhury equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) are…
A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion…
The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we…
The quasigeostrophic equation is a prototypical geophysical fluid model. In this paper, we consider time-periodic motions of this model under dissipation and time-dependent wind forcing. We show that when the wind forcing is time-periodic…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse…
We study the gravitomagnetic effect in the context of absolute parallelism with the use of a modified geodesic equation via a free parameter b. We calculate the time difference in two atomic clocks orbiting the Earth in opposite directions…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…
The deflection and gravitational lensing of light and massive particles in arbitrary static, spherically symmetric and asymptotically (anti-)de Sitter spacetimes are considered in this work. We first proved that for spacetimes whose metric…
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics,…
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time,…
Finslerian extension of the theory of relativity implies that space-time can be not only in an amorphous state which is described by Riemann geometry but also in ordered, i.e. crystalline states which are described by Finsler geometry.…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…