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In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent…
In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field…
We show that for a broad family of noncompact homogeneous Riemannian manifolds, the corresponding homogeneous Ricci flow solutions have finite extinction time, thereby confirming the dynamical Alekseevskii conjecture for these spaces. As an…
VSI (`vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants…
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual…
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that…
Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and…
We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularity representing spherically symmetric vacuum solution of the modified Ho\v{r}ava quantum gravity that is characterized by a dimensionless parameter…
In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the…
We carry on a systematic study of the physical properties of axially symmetric fluid distributions, which appear to be geodesic, shear--free, irrotational, non--dissipative and purely electric, for the comoving congruence of observers, from…
Skew-symmetric massless fields, their potentials being $r$-forms, are close analogues of Maxwell's field (though the non-linear cases also should be considered). We observe that only two of them ($r=$2 and 3) automatically yield…
We consider the electromagnetic resolution of gravitational field. We show that under the duality transformation, in which active and passive electric parts of the Riemann curvature are interchanged, a fluid spacetime in comoving…
Every evolution of a fluid is uniquely described by an energy tensor. But the converse is not true: an energy tensor may describe the evolution of different fluids. The problem of determining them is called here the {\em inverse problem}.…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
Static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor ($det.(R_{\alpha}) \neq 0$). It turns out that the only collineations…
In this work we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection enteries is taken into account for…
Charged perfect fluid with vanishing Lorentz force and massless scalar field is studied in the case of stationary cylindrically symmetric spacetime. The scalar field can depend both on radial and longitudinal coordinates. Solutions are…
A general treatment of vorticity-free, perfect fluid perturbations of Kantowski-Sachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is…
We show that if all observers see an isotropic cosmic microwave background in an expanding geodesic perfect fluid spacetime within a scalar-tensor theory of gravity, then that spacetime must be isotropic and spatially homogeneous. This…
We study Bianchi type $I$ cosmological model in the presence of magnetized anisotropic dark energy. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS $p=\omega{\rho}$ and a uniform magnetic field of energy…