Related papers: On the geodesic hypothesis in general relativity
The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field…
For gravitational-wave spacetimes of Shapovalov type III, exact general solutions of geodesic deviation equations and equations of motion of test particles are obtained. Solutions are found in a privileged coordinate system, where the…
We propose a nonlocal field theory for gravity in presence of matter consistent with perturbative unitarity, quantum finiteness, and other essential classical properties that we are going to list below. First, the theory exactly reproduces…
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic, we construct a family of metrics depending on a small…
Einstein gravity at $D\rightarrow 2$ limit can be obtained from the Kaluza-Klein procedure by taking the dimensions of the internal space to zero while keeping only the breathing mode. The resulting scalar-tensor theory can be further…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law…
We construct gravitating superconducting string solutions of the U(1)_{local} x U(1)_{global} model solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on…
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…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior spacetime of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy…
We explore some of the gravitational features of a uniform ring both in the Newtonian potential theory and in General Relativity. We use a spacetime associated to a Weyl static solution of the vacuum Einstein's equations with ring like…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n+1$-dimensional, $n \geq 3$, spatially compact spacetimes which generalizes the $k=-1$…
A special-relativistic scalar-vector theory of gravitation is presented which mimics an important class of solutions of Einstein's gravitational field equations. The theory includes solutions equivalent to Schwarzschild, Kerr,…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
The gravitational properties of the {\em only} static plane-symmetric vacuum solution of Einstein's field equations without cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field…
We study the Einstein equations coupled with the scalar field equations, $\hbox{Ein}(g)=T$, $T=T(g,\phi)+F^1$, and $\square_g\phi^\ell-m^2\phi^\ell= F^2$, where the sources $F=(F^1, F^2)$ correspond to perturbations of the physical fields…