Related papers: Geodesic Completeness around Sudden Singularities
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.
We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides,…
The equations of motion of a charged ideal fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations on a general, respectively central extension of the group of volume…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…
New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is…
In this paper we survey on some recent results on Riemannian orbifolds and singular Riemannian foliations and combine them to conclude the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations…
We consider the problem of the nature and possible types of spacetime singularities that can form during the evolution of \emph{FRW} universes in general relativity. We show that by using, in addition to the Hubble expansion rate and the…
The classical singularity theorems of R. Penrose and S. Hawking from the 1960s show that, given a pointwise energy condition (and some causality as well as initial assumptions), spacetimes cannot be geodesically complete. Despite their…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
The issue of the local visibility of the shell-focussing singularity in marginally bound spherical dust collapse is considered from the point of view of the existence of future-directed null geodesics with angular momentum which emanate…
New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the…
We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metric. Employing a 5-dimensional embedding formalism and a…
The occurrence of singularities where spacetime curvature becomes infinite and geodesic evolution breaks down are inevitable events in classical general relativity (GR) unless one chooses an exotic matter violating weak energy condition.…
In view of the well-known correspondence between gravitational fields and space-time distributions on a world manifold X, the criterion of gravitation singularities as singularities of these distributions is suggested. In the germ terms,…
Phenomenological arguments are used to explore finite-time singularity development in different physical fully-developed turbulence (FDT) situations. The role played by the cascade physics underlying this process is investigated. Such…
A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity ($\Scri{}^+$)…
Different regularizations of the Hamiltonian constraint in loop quantum cosmology yield modified loop quantum cosmologies, namely mLQC-I and mLQC-II, which lead to qualitatively different Planck scale physics. We perform a comprehensive…
In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the…
We present a complete study of the geodesics around naked singularities in AdS$_3$, the three-dimensional anti-de Sitter spacetime. These stationary spacetimes, characterized by two conserved charges --mass and angular momentum--, are…
In this paper we construct a discrete simulation of an expanding homogeneous and isotropic space-time that expands via expansion of its basic elements to figure out properties and characteristics of such a space-time and derive conclusions.…