Related papers: A 2 PN/RM metric of General Relativity
General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order…
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…
Our previous work developed a framework for treating the motion of a small body in general relativity, based on a one-parameter-family of solutions to Einstein's equation. Here we give an analysis of the coordinate freedom allowed within…
We give a pedagogical introduction into an old, but unfortunately not commonly known formulation of GR in terms of self-dual two-forms due to in particular Jerzy Plebanski. Our presentation is rather explicit in that we show how the…
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different…
We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with the energy-momentum tensor of a barotropic perfect fluid.…
The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by…
The aim of this work is to obtain new analitical solutions for Einstein equations in the anisotropical domain. This will be done via the minimal geometric deformation (MGD) approach, which is a simple and systematical method that allow us…
Gauge fields associated to the Dirac matrix algebra used with the standard quadratic gauge field Lagrangian lead to an extended gravitational Lagrangian which includes the Einstein-Hilbert one, plus quadratic, cosmological constant and…
We derive the five dimensional Myers-Perry metric via an elementary method to solve the vacuum Einstein field equations directly. This method firstly proposed by Clotz is very simple since it merely involves four components of Ricci tensor…
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field…
We discuss the linear gravitoelectromagnetic approach used to solve Einstein equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in…
This work derives the elements of classical Einstein Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin torsion field equation of EC from one…
In this paper, we found new classes of solutions to the Einstein-Maxwell field equations with matter anisotropic distribution incorporating a particular form of electric field intensity within the framework of general relativity. We use a…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
By defining a regular gauge which is conformal-like and provides instantaneous field propagation, we investigate classical solutions of (2+1)-Gravity coupled to arbitrarily moving point-like particles. We show how to separate field…