Related papers: Geodesics in the static Mallett spacetime
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy…
We prove that, generically, magnetic geodesics on surfaces will turn away from points with lightlike tangent planes, and we motivate our result with numerical solutions for closed magnetic geodesics.
In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the…
For a general spherically four--dimensional metric the notion of "circularity" of a family of equatorial geodesic trajectories is defined in geometrical terms. The main object turns out to be the angular--momentum function $J$ obeying a…
A wave-front in a space-time $\cal M$ is a family of null geodesics orthogonal to a smooth spacelike two-surface in $\cal M$; it is of some interest to know how a wave-front can fail to be a smoothly immersed surface in $\cal M$. In this…
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…
We study the geodesic motion of massless test particles in the background of a magnetic charged black hole spacetime in four dimensions in dilaton-Maxwell gravity. The behaviour of effective potential in view of the different values of…
The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide…
We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
We investigate the geodesics' kinematics and dynamics in the Linet-Tian metric with Lambda<0 and compare with the results for the Levi-Civita metric, when Lambda=0. This is used to derive new stability results about the geodesics' dynamics…
There are non-radial null geodesics emanating from the shell focusing singularity formed at the symmetric center in a spherically symmetric dust collapse. In this article, assuming the self-similarity in the region filled with the dust…
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a…
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…
Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies - limited to inhomogeneous dust cloud collapse - to more physical valid situations in which pressures are…
We investigate vacuum solutions of Einstein's equation for a universe with an S^1 topology of time. Such a universe behaves like a time-machine and has geodesics which coincide with closed time-like curves (CTCs). A system evolving along a…
Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics…