Related papers: The regularity of geodesics in impulsive pp-waves

Gravitational wave radiation from periodic orbits in some standard regular black hole spacetimes is studied, primarily using known methods (numerical and analytic). We demonstrate specific differences with the singular Schwarzschild…

We develop a general theory for linear stability of traveling waves of second order in time PDE's. More precisely, we introduce an explicitly computable index $\om^*\in (0, \infty]$ (depending on the self-adjoint part of the linearized…

We extend the classical result of Lyusternik and Fet on the existence of closed geodesics to singular spaces. We show that if $X$ is a compact geodesic metric space satisfying the CAT($\kappa $) condition for some fixed $\kappa >0$ and…

We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike $p$-brane solutions when they are lifted…

We investigate the stability of timelike Ricci curvature lower bounds under low-regularity limits of Lorentzian metrics. Specifically, we prove that the synthetic curvature-dimension condition $TCD^e_p(K,N)$, which provides an optimal…

For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer to Shapovalov's gravitational-wave models…

Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry.…

We prove optimal Lipschitz regularity of solutions to Poisson's equation with measure data supported on a $C^{1,\operatorname{Dini}}$ interface and with $C^{0,\operatorname{Dini}}$ density. We achieve this by deriving pointwise gradient…

We give a global description of envelopes of geodesic tangents of regular curves in (not necessarily convex) Riemannian surfaces. We prove that such an envelope is the union of the curve itself, its inflectional geodesics and its tangential…

We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass…

Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…

Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…

We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…

We study geodesic motion of a test particle in Schwarzschild spacetime. Bound and scattering geodesics are commonly described using Darwin variables, which provide a convenient parametrization of the radial motion. However, this description…

The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…

We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find…

Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\mu}\dd x^\mu=0$). These geodesics are studied in the exterior region of \Sch's metric.

We address the problem of finding conditions under which a compact Lorentzian manifold is geodesically complete, a property, which always holds for compact Riemannian manifolds. It is known that a compact Lorentzian manifold is geodesically…

Following the lines of a celebrated result by R. Bott (Comm. Pure Appl. Math. 9, 1956) we study the Morse index of the iterated of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic…

For a big class represented by $\theta$, we show that the metric space $(\mathcal{E}^{p}(X,\theta),d_{p})$ for $p \geq 1$ is Buseman convex. This allows us to construct a chordal metric $d_{p}^{c}$ on the space of geodesic rays in…