Related papers: Einstein's Equation in Pictures
The Einstein's equivalence principle is formulated in terms of the accuracy of measurements and its dependence of the size of the area of measurement. It is shown that different refinements of the statement 'the spacetime is locally flat'…
The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all…
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…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact solutions of Einstein equations for a scalar and massive field. The solutions have a permanent or transitory inflationary behavior.
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…
We discuss numerical solutions of Einstein's field equation describing static, spherically symmetric conglomerations of a photon gas. These equations imply a back reaction of the metric on the energy density of the photon gas according to…
By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
The Einstein-First project approaches the teaching of Einsteinian physics through the use of physical models and analogies. This paper presents an approach to the teaching of quantum physics which begins by emphasising the particle-nature…
A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…
The exact static spherically symmetric solutions for pure-aether theory and Einstein-aether theory are presented. It is shown that both theories can deliver the Schwarzschild metric, but only the Einstein-aether theory contains solutions…
Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A…
An exact solution of the Einstein equations for a Bianchi -I universe in the presence of dust, stiff matter and cosmological constant, generalising the well-known Heckmann-Schucking solution is presented. PACS: 04.20-q; 04.20.Dw Keywords:…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…
By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
We construct an asymptotic series for a general solution of the Einstein equations near a sudden singularity. The solution is quasi isotropic and contains nine independent arbitrary functions of the space coordinates as required by the…