Related papers: Some generalizations of the Raychaudhuri equation
Raychaudhuri equation is generalized in the parameterized absolute parallelism geometry. This version of absolute parallelism is more general than the conventional one. The generalization takes into account the suggested interaction between…
There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating…
I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his…
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…
The works reported in this thesis primarily address the application of the Raychaudhuri equation in two intriguing problems in gravitational physics. These problems still lack universally accepted explanations. The first problem is related…
In General Relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak…
It is shown that if the timelike eigenvector of the Ricci tensor be hypersurface orthogonal so that the space time allows a foliation into space sections then the space average of each of the scalar that appear in the Raychaudhuri equation…
In general description of the Raychaudhuri equation it is found that this first order non-linear differential equation can be written as a second order linear differential equation in the form of Harmonic Oscillator with varying frequency.…
We obtain generalized Raychaudhuri equations for spinning test particles corresponding to congruences of particle's world-lines, momentum, and spin. These are physical examples of the Raychaudhuri equation for a non-normalized vector, unit…
Specific examples of the generalized Raychaudhuri Equations for the evolution of deformations along families of $D$ dimensional surfaces embedded in a background $N$ dimensional spacetime are discussed. These include string worldsheets…
A recent generalisation of the Raychaudhuri equations for timelike geodesic congruences to families of $D$ dimensional extremal, timelike, Nambu--Goto surfaces embedded in an $N$ dimensional Lorentzian background is reviewed. Specialising…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
This study examines the formulation of a singularity theorem for timelike curves including torsion, and establishes the foundational framework necessary for its derivation. We begin by deriving the relative acceleration for an arbitrary…
A coupled system of non-linear partial differential equations is presented which describes non-perturbatively the evolution of deformations of a relativistic membrane of arbitrary dimension, $D$, in an arbitrary background spacetime. These…
We address the validity of the formalism and results presented in [ S. Das, Phys. Rev. {\bf D89} 084068 (2014)] with regard to quantum Raychaudhuri equation. The author obtained the so called quantum Raychaudhuri equation by replacing…
The present work deals with the Raychaudhuri equation (RE) to examine the space-time singularity both from classical and quantum point of view. The RE has been looked upon in terms of a classical linear Harmonic oscillator and Focusing…
It is shown that the timelike, spacelike and null versions of the Ehlers identity, as well as ensuing Raychaudhuri equations, might be all derived within a single geometrical approach based on the definition of the Riemann curvature tensor…
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…
The paper deals with the modified Raychaudhuri equation (RE) within the framework of homogeneous and isotropic Fractal Universe. Focusing of a congruence of time-like geodesics has been examined for three generic choices of the fractal…
Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent…