Related papers: Einstein's Equation in Pictures
How to effectively solve the eigen solutions of the nonlinear spinor field equation coupling with some other interaction fields is important to understand the behavior of the elementary particles. In this paper, we derive a simplified form…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
The Einsteins Machian Program is here accomplished.
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
From a particularly simple solution of the Ernst equation, we build a solution of the vacuum stationary axisymmetric Einstein equations depending on three parameters. The parameters are associated to the total mass of the source and its…
Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in…
A solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects, and may also provide a description of our universe on length scales…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…
The Einstein-Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self…
Einstein's revolutionary light quantum hypothesis of 1905 and his further contributions to quantum theory are reviewed.
This paper reconstructs the derivations underlying the kinematical part of Einstein's 1905 special relativity paper, emphasizing their operational clarity and minimalist use of mathematics. Einstein employed modest tools-algebraic…
We present cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells. Positivity of the energy density of the thin…
The relationships among various parameters describing the strength of optical transitions in atoms and molecules are reviewed. The application of these parameters to the description of the interaction between nearly monochromatic,…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is…
In this paper, we expose the construction of a possible, simple quantum matrix group (according to Woronowicz), related to elementary formal aspects of the Einstein field equations of General Relativity, and its possible symmetries.
This paper explores the ER bridges theory and its relationship with quantum phenomena. An argument can be made that the ER bridges theory does not explicitly address quantum phenomena and implies that Einstein intended to differentiate…
We study a numerical solution to Einstein's equation for a compact object composed of null particles. The solution avoids quantum scale regimes and hence neither relies upon nor ignores the interaction of quantum mechanics and gravitation.…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…