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We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
A new exact static interior solution of the Einstein equations is obtained for a gravitating ball filled with a Pascal perfect fluid . The solution is an extension of the well-known interior solution with a parabolic distribution of mass…
We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of…
The spherically symmetric, static spacetime generated by a crossflow of non-interacting radiation streams, treated in the geometrical optics limit (null dust) is equivalent to an anisotropic fluid forming a radiation atmosphere of a star.…
By analyzing the Einstein's equations for the static sphere, we find that there exists a non-singular static configuration whose radius can approach its corresponding horizon size arbitrarily.
We analyze the isothermal property in static fluid spheres within the framework of the modified $f(R, T)$ theory of gravitation. The equation of pressure isotropy of the standard Einstein theory is preserved however, the energy density and…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
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 demonstrate that the Einstein relation for the diffusion of a particle in the random energy landscape with the Gaussian density of states is an exclusive 1D property and does not hold in higher dimensions. We also consider the analytical…
By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
McVittie's spacetime is a spherically symmetric solution to Einstein's equation with an energy-momentum tensor of a perfect fluid. It describes the external field of a single quasi-isolated object with vanishing electric charge and angular…
The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…
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 analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear…
We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…
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…
For the cylindrically symmetric ''asymptotically flat'' Einstein equations in the case of electro-vacuum it is known that solutions exist globally and also that this class of spacetimes is causally geodesically complete. Hence strong cosmic…