相关论文: Raychaudhuri and optical equations for null geodes…
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy the critical convexity inequality of…
We argue that compatibility with elementary particle physics requires gravitational theories with torsion to be unable to distinguish between orbital angular momentum and spin. An important consequence of this principle is that spinless…
The paper aims at deriving a curvature form of the famous Raychaudhuri equation (RE) and the associated criteria for focusing of a hyper-surface orthogonal congruence of time-like geodesic. Moreover, the paper identifies a transformation of…
The field equation of orthodox general relativity are written in the context of a geometry with non-vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological…
Several exact cosmological solutions of a metric-affine theory of gravity with two torsion functions are presented. These solutions give a essentially different explanation from the one in most of previous works to the cause of the…
We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and…
The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy-momentum deposit of the chosen gravitational system. This is pursued…
Torsion is a non-Riemannian geometrical extension of general relativity that allows including the spin of matter and the twisting of spacetime. Cosmological models with torsion have been considered in the literature to solve problems of…
Although the autoparallel curves and the geodesics coincide in the Riemannian geometry in which only the curvature is nonzero among the nonmetricity, the torsion and the curvature, they define different curves in the non-Riemannian ones. We…
Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to…
For the Newtonian N-body problem, we study the Jacobi-Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the distances between the bodies must be divergent functions. More…
Recently, we introduced the Lorentzian-Euclidean black hole, a static and spherically symmetric solution of vacuum Einstein equations that exhibits a change in metric signature across the event horizon. In this framework, the analysis of…
We study cosmological consequences of the dark spinor model when torsion is included. Only some components of the torsion are allowed to be non-vanishing in homogeneous and isotropic cosmology, but there exist freedoms in the choice of…
Spacetimes with everywhere vanishing curvature tensor, but with torsion different from zero only on world sheets that represent closed loops in ordinary space are presented, also defects along open curves with end points at infinity are…
We study photon orbits in the background of $(1+3)$-dimensional static, spherically symmetric geometries. In particular, we have obtained exact analytical solutions to the null geodesic equations for light rays in terms of the…
In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and…
We perform observational confrontation and cosmographic analysis of $f(T,T_G)$ gravity and cosmology. This higher-order torsional gravity is based on both the torsion scalar, as well as on the teleparallel equivalent of the Gauss--Bonnet…
The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general…
The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics…
Hamilton and Moitra (2021) showed that, in certain regimes, it is not possible to accelerate Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms which make queries in a (large) bounded domain and which…