Related papers: Stress and Geometry for Isotropic Singularities
Various theoretical obstacles are associated with a homogeneous and isotropic distribution of ``charge'' which is subject to a repulsive, long-range force. We show how these can be overcome, for all practical purposes, by the simple device…
We review our study of Sasakian geometry as an agent for proving the existence of Einstein metrics on odd dimensional manifolds. Particular emphasis is given to the Sasakian structures occuring on links of isolated hypersurface…
In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalised) Robertson-Walker space-time is important. In particular, it is a requirement for the development…
A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time,…
We make precise the heretofore ambiguous statement that anisotropic stress is a sign of a modification of gravity. We show that in cosmological solutions of very general classes of models extending gravity --- all scalar-tensor theories…
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate…
We consider a spacetime singularity at $t = 0$ arising in a Kasner-type metric that solves the gravitational equations modified by quantum effects of a conformal field theory (CFT). The resulting constraints can be solved efficiently when…
In this work we have proposed some spherically symmetric, static spacetimes in a theory of gravity which permits non-minimal coupling (NMC) between curvature of spacetime and fluid variables. It is shown that these non-minimally coupled…
We derive the equations of motion for scalar metric perturbations in a particular nonsingular bouncing cosmology, where the big bang singularity is replaced by a spacetime defect with a degenerate metric. The adiabatic perturbation solution…
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely…
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case…
The large-scale structure of the Universe is a rich source of information to test the consistency of General Relativity on cosmological scales. We briefly describe how the observed distributions of galaxies is affected by redshift-space…
Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are…
In this article we propose to add stress-energy tensor to the Einstein equations, assuming that the matter-energy and the metric space-time is nothing but a continuous medium with some elastic properties. We first give a general expression…
Using a metric-based formalism to treat cosmological perturbations, we discuss the connection between anisotropic stress on the brane and brane bending. First we discuss gauge-transformations, and draw our attention to gauges, in which the…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular…