Related papers: Discrete and finite Genral Relativity
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are…
One of the highlight of this note is that the author presents the relativistic gravity field that Einstein was looking for. The field is a byproduct of the matter in motion. This field can include both the discrete and continuous…
We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst…
Gravity is a phenomenon which arises due to the space-time geometry. The main equations that describe gravity are the Einstein equations. To understand the consequences of these field equations we need to calculate the free particle…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
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…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
The so-called $\Gamma\Gamma$-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…
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…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
Beginning from the Ashtekar formulation of canonical general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by gauge-fixing the gravitational fields within a complex of…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac $\delta$-function, including a description of a continuous collapse to such a point mass, is given. A…
Among relativistic theories of gravitation the closest ones to general relativity are the scalar-tensor ones and these with Lagrangians being any function f(R) of the curvature scalar. A complete chart of relationships between these…