Related papers: Congruence Convergence in pp-wave Spacetime
The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The role of twist in the relation of the Rosen coordinates adapted to a null congruence…
The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion,…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
Implications of the Raychaudhuri equation in focusing of geodesic congruences are studied in the framework of scalar--tensor theory of gravity. Specifically, we investigate the Brans--Dicke theory and Bekenstein's scalar field theory. In…
In the present work some generalizations of the Hawking singularity theorems in the context of $f(R)$ theories are presented. The assumptions are of these generalized theorems is that the matter fields satisfy the conditions…
We describe impulsive gravitational pp-waves entirely in the distributional picture. Applying Colombeau's nonlinear framework of generalized functions we handle the formally ill-defined products of distributions which enter the geodesic as…
We investigate the vacuum pp-wave and Aichelburg-Sexl-type solutions in f(R) and the modified Gauss-Bonnet theories of gravity with both minimal and nonminimal couplings between matter and geometry. In each case, we obtain the necessary…
Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers.…
A non-linear gravitational wave imparts gravitational acceleration to all particles that are hit by the wave. We evaluate this acceleration for particles in the pp-wave space-times, and integrate it numerically along the geodesic…
The cosmological propagation of tensor perturbations is studied in the context of parity-violating extensions of the symmetric teleparallel equivalent of General Relativity theory. This non-Riemannian formulation allows for a wider variety…
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…
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and…
The detection of gravitational waves (GWs) propagating through cosmic structures can provide invaluable information on the geometry and content of our Universe, as well as on the fundamental theory of gravity. In order to test possible…
A possible generalization of plane fronted waves with parallel rays (gpp-wave) fall into a more general class of metrics admitting parallel null 1-planes. For gpp-wave metric, the zero-curvature condition is given, the Killing-Yano tensors…
Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on…
Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski, where he obtains local…
The family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
The geometry of P, the bundle of null directions over an Einstein space-time, is studied. The full set of invariants of the natural G-structure on P is constructed using the Cartan method of equivalence. This leads to an extension of P…
In this short paper, Penrose's famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose's singularity theorem are not satisfied as the space-time is not…