Related papers: Einstein's Equation in Pictures
The aim of this work is to show how Einstein's quantum hypothesis leads immediately and necessarily to a departure from classical mechanics. First we note that the classical description and predictions are in terms of idealized measurements…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
We provide a compendium of the quantum mechanical equations for photon emission rates, photon absorption cross sections, and photon scattering cross sections. For each case, the different equations that apply for discrete or continuous…
Einstein's 1905 derivation of E = mc^2 has been criticized for being circular. Although such criticisms have been challenged it is certainly true that the reasoning in Einstein's original derivation is not at all obvious. Einstein's…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which…
The Ashtekar-Renteln Ansatz gives the self-dual solutions to the Einstein equation. A direct generalization of the Ashtekar-Renteln An\-satz to N=1 supergravity is given both in the canonical and in the covariant formulation and a…
In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward…
We present in this article a general approach (in the form of recommendations and guidelines) for tackling Diophantine equation problems (whether single equations or systems of simultaneous equations). The article should be useful in…
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are…
In modern physics courses the idea of photon has been teaching through from the einsteinian formulation based on the photoelectric effect. Einstein's photon concept allow the quantization of the electromagnetic field, but does not dwell on…
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity…
We treat the semiclassical Einstein equation as a quantum-classical hybrid and demonstrate the formal equivalence of its two derivation methods. This approach identifies the left-hand side of the equation as the expectation value of the…
I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence,…
A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that…
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the…
In recent years, interest in extra dimensions has experienced a dramatic increase. A common practice has been to look for higher-dimensional generalizations of four-dimensional solutions to the Einstein equations. In this vein, we have…
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…