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Recent developments in observational cosmology have led to attempts to make modifications on both sides of the Einstein equation to explain some of the puzzling new findings. What follows is an examination of the source of gravity that we…
We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a…
The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric.…
A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
We present two new solutions to Einstein's equations in (1+5)-spacetime with a positive bulk cosmological constant. One solution has increasing and another solution decreasing bounded scale function without singularities in the range from…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
We study the Einstein-Lichnerowicz constraints system, obtained through the conformal method when addressing the initial data problem for the Einstein equations in a scalar field theory. We prove that this system is stable with respect to…
We discuss several results in electrostatics: Onsager's inequality, an extension of Earnshaw's theorem, and a result stemming from the celebrated conjecture of Maxwell on the number of points of electrostatic equilibrium. Whenever possible,…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
Some properties of an exact solution due to Vaidya, describing the gravitational field produced by a point particle in the background of the static Einstein universe are examined. The maximal analytic extension and the nature of the…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for…
In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the…
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…
The Einstein gravitational field of a material point at rest is derived anew - by a suitable limit process - from the field of a sphere of a homogeneous and incompressible fluid. This result supports clearly the thesis according to which…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy…