Related papers: Kinematics of geodesic flows in stringy black hole…
We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded with quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear…
We study the kinematics of timelike geodesic congruences, in the spacetime geometry of rotating black holes in three (the BTZ) and four (the Kerr) dimensions. The evolution (Raychaudhuri) equations for the expansion, shear and rotation…
We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the Raychaudhuri equation for expansion scalar as an initial value problem. The…
In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…
We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations.…
We introduce an exactly solvable example of timelike geodesic motion and geodesic deviation in the background geometry of a well-known two-dimensional black hole spacetime. The effective potential for geodesic motion turns out to be either…
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)…
A recent notion of geodesic flows which comes out of noncommutative geometry but which is also novel in the classical case is studied in detail for a Schwarzschild spacetime. In this framework, the geodesic velocity field is an independent…
We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test…
Raychaudhuri equation is derived by assuming geometric flow in spacetime M of n+1 dimensions. The equation turns into a harmonic oscillator form under suitable transformations.Thereby a relation between geometrical entropy and mean geodesic…
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,…
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…
I present some applications of geometric flows in string theory and gravity. In some circumstances time evolution in string theory can be approximately identified with Ricci-flow parametric evolution of spatial sections. In four dimensions,…
We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy…
We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions…
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null…
In a given geometry, the kinematics of a congruence of curves is described by a set of three quantities called expansion, rotation, and shear. The equations governing the evolution of these quantities are referred to as kinematic equations.…
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…
Exploring the characterization of singular black hole spacetimes, we study the relation between energy density, curvature invariants, and geodesic completeness using a quadratic $f(R)$ gravity theory coupled to an anisotropic fluid. Working…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…