Related papers: Finding and using exact solutions of the Einstein …
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
We consider the interaction of gravity, as expressed by Einstein's Equations of General Relativity, to other force fields. We describe some recent results, discussing both the mathematics, and the physical interpretations. These results…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore,…
Albert Einstein's journey to formulate the theory of general relativity involved significant shifts in his approach to gravitational field equations. Starting in 1912, he collaborated with Marcel Grossmann and initially explored broadly…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
In the last 100 years, the most important equations in physics are Maxwell's equations for electrodynamics, Einstein's equation for gravity, Dirac's equation for the electron and Yang-Mills equation for elementary particles. Do these…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
Symmetric gauge fields and invariant metrics in homogeneous spaces are found. Their use for finding exact solutions of the Einstein-Yang-Mills (EYM) equations is discussed.
It is offered another method how to describe contemporary stage of the Universe evolution. The method is based upon classical Einstein equations without a dark energy and other hypothetical fields.
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
Five classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. These are plane waves and their collisions, cylindrical waves, Robinson-Trautman and type N spacetimes, boost-rotation…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
I present a new method to generate rotating solutions of the Einstein-Maxwell equations from static solutions, give several examples of its application, and discuss its general properties.
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
It is shown that in the weak field approximation solutions of Brans-Dicke equations are simply related to the solutions of General Relativity equations for the same matter distribution. A simple method is developed which permits to obtain…
The gravitational field of an idealized plane-wave solution of the Maxwell equations can be described in closed form. After discussing this particular solution of the Einstein-Maxwell equations, the motion of neutral test particles, which…