Related papers: Properties of kinematic singularities
Spatially homogeneous and anisotropic Bianchi type V space-time with bulk viscous fluid source and time varying gravitational constant $G$ and cosmological term $\Lambda$ are considered. Coefficient of bulk viscosity $\zeta$ is assumed as a…
We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be…
We show under the assumption of small data that solutions to the Einstein-Vlasov system with a pure magnetic field and Bianchi I symmetry isotropise and tend to dust solutions. We also obtain the decay rates for the main variables. This…
Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
A viable spacetime is one that admits a complete timelike geodesic. It is shown that a causal diffeomorphism preserving the Ricci tensor between two spacetimes is necessarily a homothety, if one of them is viable.
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity,…
The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant…
Ricci flow spacetimes were introduced by Kleiner & Lott as a way to describe Ricci flow through singularities, and have since been used elsewhere in the literature, prompting the question of their rigidity. In $(2+1)$-dimensions, we show…
The present study deals with spatially homogeneous and totally anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with variable $G$ and $\Lambda$ in presence of imperfect fluid. To get the deterministic model…
Spacetimes with a vanishing second Ricci invariant, but which are not necessarily Ricci - flat, though common in general relativity, are seldom studied in a coordinate and symmetry independent way by actually using their Ricci invariants.…
We demonstrate analytically and numerically the existence of geodesically complete singularities in quintessence and scalar tensor quintessence models with scalar field potential of the form $V(\phi)\sim \vert \phi\vert^n$ with $0<n<1$. In…
We explore the connection of a general relativistic matter-energy momentum tensor with the polynomial degeneracies of higher order curvature invariants defined in Riemannian geometry. The degeneracies enforce additional constraints on the…
The multidimensional cosmological model describing the evolution of $n$ Einstein spaces in the presence of multicomponent perfect fluid is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the…
In this paper, we study the Ricci flow on a closed manifold of dimension $n \ge 4$ and finite time interval $[0,T)~(T < \infty)$ on which the scalar curvature are uniformly bounded. We prove that if such flow of dimension $4 \le n \le 7$…
In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein's equations consisting in a ($N+2$)-dimensional static and hyperplane symmetric perfect fluid satisfying the…
What restrictions are there on a spacetime for which the Ricci curvature is such as to produce convergence of geodesics (such as the preconditions for the Singularity Theorems) but for which there are no singularities? We answer this…
In this paper, a spatially homogeneous and anisotropic Bianchi type V model filled with an imperfect fluid with bulk viscosity and particle creation, is investigated within the framework of General Relativity. Particle creation and bulk…
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field \xi are discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field \xi are determined. Conditions for the Ricci soliton…