Related papers: Congruence Convergence in pp-wave Spacetime
We investigate exact plane-fronted gravitational wave (pp-wave) solutions within the framework of shift-symmetric quadratic-order higher-order scalar--tensor (HOST) theories. These solutions represent fully nonlinear radiative spacetimes…
The Noether gauge symmetries of geodesic Lagrangian for the pp-wave spacetimes are determined in each of the Noether gauge symmetry classes of the pp-wave spacetimes. It is shown that a type N pp-wave spacetime can admit at most three…
In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall--Sundrum AdS (Anti de Sitter)…
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of…
We investigate a class of gravitational pp-waves which represent the exterior vacuum field of spinning particles moving with the speed of light. Such exact spacetimes are described by the original Brinkmann form of the pp-wave metric…
We introduce and develop the 1+3 covariant approach to relativity and cosmology to spacetimes of arbitrary dimensions that have nonzero torsion and do not satisfy the metricity condition. Focusing on timelike observers, we identify and…
In this paper we introduce a new approach to the study of the effects that an impulsive wave, containing a mixture of material sources and gravitational waves, has on a geodesic congruence that traverses it. We find that the effect of the…
We present the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves) that are of algebraic type III and for which the cosmological constant ($\Lambda_c$) is non-zero.…
We investigate a particular regularization of big bang singularity, which remains within the domain of 4-dimensional general relativity but allowing for degenerate metrics. We study the geodesics and geodesic congruences in the modified…
It has been known that the propagation of sound in fluids can be used to model acoustic spacetimes. These acoustic spacetimes offer analogue models for gravity. We use the Raychaudhuri equation to study the propagation of sound in these…
We shall investigate the properties of a congruence of geodesics in the framework of Palatini f(R) theories. We shall evaluate the modified geodesic deviation equation and the Raychaudhuri's equation and show that f(R) Palatini theories do…
The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized…
Global geometric properties of product manifolds ${\cal M}= M \times \R^2$, endowed with a metric type $<\cdot, \cdot > = < \cdot, \cdot >_R + 2 dudv + H(x,u) du^2$ (where $<\cdot, \cdot >_R$ is a Riemannian metric on $M$ and $H:M \times \R…
We prove that any real, vacuum gravitational perturbation of a 4-dimensional vacuum pp-wave space-time can be locally expressed, modulo gauge transformations, as the real part of a Hertz/Debye potential, where the scalar potential satisfies…
In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and…
We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem with a Neumann boundary condition. The geometry is symmetric…
Plane waves are a special class of Lorentzian spaces with a parallel null vector field. They are of great importance in Geometry (e.g. Lorentzian holonomy) and in Physics (General Relativity as well as alternative gravity theories). Our…
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.
Taking a quantum corrected form of Raychaudhuri equation in a geometric background described by a Lorentz-violating massive theory of gravity, we go through investigating a time-like congruence of massive gravitons affected by a Bohmian…
We analyse the relation between two a priori quite different expansions of the string equations of motion and constraints in a general curved background, namely one based on the covariant Penrose-Fermi expansion of the metric G_{\mu\nu}…