Related papers: Geodesics of simultaneity in Schwarzschild

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…

In this paper we study geodesics of left-invariant sub-Riemannian metrics on SO(3) and almost-Riemannian metrics on $S^2$. These structures are connected with each other, and it is possible to use information about one of them to obtain…

The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…

We prove that every complete Einstein (Riemannian or pseudo-Riemannian) metric $g$ is geodesically rigid: if any other complete metric $\bar g$ has the same (unparametrized) geodesics with $g$, then the Levi-Civita connections of $g$ and…

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric. We study the…

Streamlines of a relativistic perfect isentropic fluid are geodesics of a Riemannian space whose metric is defined by enthalpy of the fluid. This fact simplifies the solution of some problems, as is also of interest from the point of view…

For gravity coupled to N scalar fields with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N+1)-dimensional `augmented' target space of Lorentzian signature (1,N),…

A technique for generating spherically symmetric dislocation solutions of a direct Poincar\'{e} gauge theory of gravity based on homogeneous functions which makes Cartan torsion to vanish is presented.Static space supported dislocation and…

We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces $M=G/K$ whose isotropy representation decomposes into a direct sum of three submodules…

Space-times admitting a shear-free, irrotational, geodesic null congruence are studied. Attention is focused on those space-times in which the gravitational field is a combination of a perfect fluid and null radiation.

There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past…

Given a metric space $X$ and a subspace $A\subset X$, we prove $A$ can generate various algebraic elements in persistent homology of $X$. We call such elements (algebraic) footprints of $A$. Our results imply that footprints typically…

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…

Magnitude homology is an $\mathbf{R}^+$-graded homology theory of metric spaces that captures information on the complexity of geodesics. Here we address the question: when are two metric spaces magnitude homology equivalent, in the sense…

This paper studies the situation when two 4-dimensional Lorentz manifolds (that is, space-times) admit the same (unparametrised) geodesics, that is, when they are projectively related. A review of some known results is given and then the…

We study the behaviour of geodesics on a Riemannian manifold near a generalized conical or cuspidal singularity. We show that geodesics entering a small neighbourhood of the singularity either hit the singularity or approach it to a…

We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…

Schwarzschild black hole is the simplest black hole that is studied most in detail. Its behavior is best understood by looking at the geodesics of the particles under the influence of its gravitational field. In this paper, the focus of…

This is a consecutive paper on the timelike geodesic structure of static spherically symmetric spacetimes. First we show that for a stable circular orbit (if it exists) in any of these spacetimes all the infinitesimally close to it timelike…

The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…