相关论文: Geodesics of simultaneity in Schwarzschild

In the framework of Lorentzian multiply warped products we study the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) spacetime near hypersurfaces in the interior of the event horizon. We also investigate the geodesic motion in…

Propagation of light in nonlinear materials is here studied in the regime of the geometrical optics. It is shown that a spherically symmetric medium at rest with some specific dielectric properties can be used to produce an exact analogue…

It is shown that a timelike radial geodesic does not become null at the event horizon

The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of…

This short survey illustrates the ideas of Teichmuller dynamics. As a model application we consider the asymptotic topology of generic geodesics on a "flat" surface and count closed geodesics and saddle connections. This survey is based on…

The aim of this paper is to extend the definition of geodesics to conical manifolds, defined as submanifolds of $\R^n$ with a finite number of singularities. We look for an approach suitable both for the local geodesic problem and for the…

It has been established in Schwarzschild spacetime (and more generally in Kerr spacetime) that pairs of geometrically different timelike geodesics with the same radial and azimuthal frequencies exist in the strong field regime. The…

The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as…

By using simplified 2D gravitational, non-local Lorentz invariant actions constructed upon the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a…

Gravitational waves with parallel rays are known to have remarkable properties: Their orbit space of null rays possesses the structure of a non-relativistic spacetime of codimension-one. Their geodesics are in one-to-one correspondence with…

In this paper we investigate possible extensions of the idea of geodesic completeness in complex manifolds, following two directions: metrics are somewhere allowed not to be of maximum rank, or to have 'poles' somewhere else. Geodesics are…

A homogeneous Riemannian manifold $(M=G/K, g)$ is called a space with homogeneous geodesics or a $G$-g.o. space if every geodesic $\gamma (t)$ of $M$ is an orbit of a one-parameter subgroup of $G$, that is $\gamma(t) = \exp(tX)\cdot o$, for…

The linear stability of closed timelike geodesics (CTGs) is analyzed in two spacetimes with cylindrical sources, an infinite rotating dust cylinder, and a cylindrical cloud of static cosmic strings with a central spinning string. We also…

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…

Let (X,\omega) be a compact K\"ahler manifold. As discovered in the late 1980s by Mabuchi, the set H_0 of K\"ahler forms cohomologous to \omega has the natural structure of an infinite dimensional Riemannian manifold. We address the…

The geodesic flow on a finite discrete q-manifold with or without boundary is defined as as a permutation of its ordered q-simplices. This allows to define geodesic sheets and a notion of sectional curvature.

This article aims at comparing gravitational wave memory effect in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating…

Two metrics on a manifold are geodesically equivalent if sets of their unparameterized geodesics coincide. In this paper we show that if two left $G$-invariant metrics of arbitrary signature on homogenous space $G/H$ are geodesically…

We consider the nonlinear Schr\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the…

We study the geodesics of the singularity free metric considered in the preceding Paper I and show that they are complete. This once again demonstrates the absence of singularity. The geodesic completeness is established in general without…