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An extended test body moving in a curved spacetime does not typically follow a geodesic, because of forces that arise from couplings between its multipole moments and the ambient curvature. An illustration of this fact was provided by…
Alternative theories of gravity not only modify the polarization contents of the gravitational wave, but also affect the motions of the stars and the energy radiated away via the gravitational radiation. These aspects leave imprints in the…
A simple 1D dynamical model of thermally driven disc winds is proposed, based on the results of recent, 2.5D axi-symmetric simulations. Our formulation of the disc wind problem is in the spirit of the original Parker (1958) and Bondi (1952)…
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin…
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
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…
We take a three dimensional Euclidian metric in toroidal coordinates and consider the corresponding Laplace equation. The simplest solution of this equation is taken. Based on this we build a Weyl space-time. This space-time is transformed…
The Gibbons-Werner method for calculating deflection angles using the Gauss-Bonnet theorem and optical/Jacobi metric has become widely popular in recent years. Werner extended this method to stationary spacetimes, where the optical/Jacobi…
Gravitational waves affect the observed direction of light from distant sources. At telescopes, this change in direction appears as periodic variations in the apparent positions of these sources on the sky; that is, as proper motion. A wave…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
A timelike splitting theorem for Finsler spacetimes was previously established by the third author, in collaboration with Lu and Minguzzi, under relatively strong hypotheses, including the Berwald condition. This contrasts with the more…
We generalize the notion of Zermelo navigation to arbitrary pseudo-Finsler metrics possibly defined in conic subsets. The translation of a pseudo-Finsler metric $F$ is a new pseudo-Finsler metric whose indicatrix is the translation of the…
We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian…
The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an…
We consider higher-dimensional generalizations of the $\alpha$-Grushin plane, focusing on the problem of classification of geodesics that minimize length, also known as optimal synthesis. Solving Hamilton's equations on these spaces using…
We compute the mass and current quadrupole tidal corrections to the four-momentum and energy flux radiated during the scattering of two spinless bodies, at leading order in $G$ and at all orders in the velocities, using the effective field…
Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold…
We present a novel test of general relativity (GR): measuring the geometric component of the time delay due to gravitational lensing. GR predicts that photons and gravitational waves follow the same geodesic paths and thus experience the…
We consider the release from a point source of relatively heavy fluid into a porous saturated medium above an impermeable slope. We consider the case where the volume of the resulting gravity current increases with time like $t^\alpha$ and…
We study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated…