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This paper explores the quantum-fluid correspondence in a charged relativistic fluid with intrinsic spin. We begin by examining the nonrelativistic case, showing that the inclusion of spin introduces a quantum correction to the classical…
In this paper we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes and produce an example to verify the existence of such a spacetime. Then we demonstrate that a conformally flat generalized Ricci-recurrent…
The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the…
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which…
We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian…
The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a `kinematic singularity' at which the fluid congruence is inextendible but…
We present the conformally 1+3 Hubble-normalized field equations together with the general total source equations, and then specialize to a source that consists of perfect fluids with general barotropic equations of state. Motivating,…
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as…
The geometric flow theory and its applications turned into one of the most intensively developing branches of modern geometry. Here, a brief introduction to Finslerian Ricci flow and their self-similar solutions known as Ricci solitons are…
We have found exact constant solutions for the cosmological density parameter using a generalization of general relativity that incorporates a cosmic time-variation of the velocity of light in vacuum and the Newtonian gravitation constant.…
The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the…
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity…
A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the…
Rainich-type conditions giving a spacetime "geometrization" of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and…
We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light. In order to perform this expansion it…
We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and…
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic…
In this paper, we analyze a two coupled fluids model by investigating several solutions for accelerated universe in flat FRW space-time. One of the fluids can be identified with the matter and the model possesses the standard matter…
Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change…
Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are…