Related papers: Effective null Raychaudhuri equation
We study the singularity of the congruences for both timelike and null geodesic curves using the expansion of the early anisotropic Bianchi type I Universe. In this paper, we concentrate on the influence of the shear of the timelike and…
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 examine whether the Schwarzschild black hole can emerge as the continuous end state of gravitational collapse from a non-singular configuration. Employing a time dependent extension of the regular Schwarzschild metric, we track the…
Spacetime singularities are studied in both the $D+d$-dimensional string theory and its $D$-dimensional effective theory, obtained by the Kaluza-Klein compactification. It is found that spacetime singularities in the low dimensional…
We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered…
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…
In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the…
In a previous paper [9], we proved the following singularity theorem applicable to cosmological models with a positive cosmological constant: if a four-dimensional spacetime satisfying the null energy condition contains a compact Cauchy…
Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this ends a…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
Can global internal and spacetime symmetries be connected without supersymmetry? To answer this question, we investigate Minkowski spacetimes with d space-like extra dimensions and point out under which general conditions external…
We use the phenomenological approach to study properties of space-time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that…
We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends…
A class of curves with special conformal properties (conformal curves) is studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data for the conformal curves can be prescribed so that the resulting congruence of curves…
We study the near-horizon spacetime for isolated and dynamical trapping horizons (equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing Gaussian null coordinate and the terms of that expansion are…
Extended gravitational models have gained large attention in the last couple of decades. In this work, we examine the solution space of vacuum, static, and spherically symmetric spacetimes within $F(R)$ theories, introducing novel methods…
Quantum gravity effects modify the Heisenberg's uncertainty principle to a generalized uncertainty principle (GUP). Earlier work showed that the GUP-induced corrections to the Schr\"odinger equation, when applied to a non-relativistic…
We studied the Raychaudhuri equation in Kaluza-Klein space-time. We derived an additional term that is solely due to Kaluza-Klein's unification. This term affects the defocus of world lines near the singularity of charged higher-dimensional…
New physics beyond General Relativity impacts black-hole spacetimes. The effects of new physics can be investigated in a largely theory-agnostic way by following the principled-parameterized approach. In this approach, a classical…