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The present paper has the purpose to illustrate the importance of the ideas and constructions of the Non-Euclidean (Lobachevsky) Geometry, which can be applied even today for solving some conceptually important problems. We study the static…
The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black…
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Tiwari 1984, Gautreau…
We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state $ P=-\rho/5$. These geometries depend on up to four parameters and are static…
In this thesis four separate problems in general relativity are considered, divided into two separate themes: coordinate conditions and perfect fluid spheres. Regarding coordinate conditions we present a pedagogical discussion of how the…
Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
In this paper we analyze spherically symmetric static vacuum solutions with various topologies in mimetic gravity. When the Einstein's tensor is different from zero, a new class of solutions different from the Schwarzschild one emerges from…
An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of…
A new solution with constant torsion is derived using the field equations of f(T). Asymptotic forms of energy density, radial and transversal pressures are shown to meet the standard energy conditions, i.e., weak and null energy conditions…
Two new classes of exact interior static solutions of the Einstein equations in homogeneous coordinates for a gravitating ball filled by a Pascal perfect fluid are obtained. Schwarzschild's interior solution of is a special case of these…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
In this work we present an exact solution of the Einstein-Maxwell field equations describing compact, charged objects within the framework of classical general relativity. Our model is constructed by embedding a four-dimensional spherically…
A Spin-polarised cylindrically symmetric exact class of solutions endowed with magnetic fields in Einstein-Cartan-Maxwell gravity is obtained. Application of matching conditions to this interior solution having an exterior as Einstein's…
A new exact solution of the Einstein-Maxwell equations for the gravitational collapse of a shell of matter in an already formed black hole is given. Both the shell and the black hole are endowed with electromagnetic structure and are…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…