Related papers: On generalized quasi-Einstein GRW space-times
In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled…
This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal…
A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…
Gravity whose nature is fundamental to the understanding of solar system, galaxies and the structure and evolution of the Universe, is theorized by the assumption of curved spacetime, according to Einstein`s general theory of relativity…
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…
We generalize our previous theorem for FLRW spacetimes within the framework of generic metric gravity theories. In earlier work, we proved that, in the absence of matter fields, the field equations of any metric gravity theory constructed…
We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In…
We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson-Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On…
It is proved in the manuscript that as long as the proper coordinate transformation is introduced,, the equations of geodetic lines described in curved space-time can be transformed into the dynamic equations in flat space-time, that is to…
In the $R+\alpha R^2$ gravity theory, we show that if freely propagating massless particles have an almost isotropic distribution, then the spacetime is almost Friedmann-Robertson-Walker (FRW). This extends the result proved recently in…
We review recent work on the Einstein equations of general relativity when the curvature is defined in a weak sense. Weakly regular spacetimes are constructed, in which impulsive gravitational waves, as well as shock waves, propagate.
In this paper we study the higher dimensional homogeneous and isotropic perfect fluid spacetimes in Einstein-Gauss-Bonnet (EGB) gravity. We solve the modified field equations with higher order curvature terms to determine the evolution of…
In the present paper we discuss about a set of geometric properties and physical applications of a mixed quasi-Einstein spacetime$[M(QE)_{4}]$, which is a special type of nearly quasi-Einstein spacetime$[N(QE)_{4}]$. Firstly we consider a…
We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. These…
In this paper the application of the $M$-projective curvature tensor in the general theory of relativity has been studied. Firstly, we have proved that an $M$-projectively flat quasi-Einstein spacetime is of a special class with respect to…
While it is generally agreed that the nature of spacetime must be drastically different at the Planck scale, it has been a common practice to assume that spacetime is endowed with a full pseudo-Riemannian geometry regardless of the physical…
The aim of this paper is to extend the notion of all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed generalized quasi-Einstein manifold, pseudo generalized quasi-Einstein manifold and many more and name it…
We analyze the global nonlinear stability of FRW (Friedmann-Robertson-Walker) spacetimes in presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state relating…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…
We summarize recent results on $D$-dimensional Robinson-Trautman solutions of Einstein's gravity in the presence of a conformally invariant non-linear electromagnetic field and a cosmological constant. These spacetimes contain static dyonic…