Einstein-Klein-Gordon System in Higher Dimensional

In this present work, we study the Einstein equation coupled with the nonlinear Klein-Gordon equation. We obtain Ricci tensor, scalar curvature, and Einstein equation of the Einstein-Klein-Gordon system in higher dimensional. If we put D=4, our formulations reduce to the four dimensional Einstein-Klein-Gordon system.

Newman-Janis Ansatz for rotating wormholes

A central problem in General Relativity is obtaining a solution to describe the source’s interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by the Newman-Janis to generate solutions to the Einstein field equation inspired by the mention problems. We present a collection of independent classes of exact interior solutions of the Einstein equation describing rotating fluids with anisotropic pressures. Furthermore, we will elaborate on some obtained solutions by alluding to rotating wormholes.

Safe Distance Mathematical Calculation and Quantitative Analysis on Covid-19 Using Einstein Equation and Gaussian Distribution

Most of the diseases caused by virus mainly spread through droplets in the air. The pathogen bearing droplets go deep into people’s lungs and cause infection. In this paper, we analyze the safe distance, the minimum range to keep droplets containing virus particles from entering lungs, and thereby carrying the virus inside the lung. Einstein equation for diffusivity of a particle and the wide of the Gaussian distribution of the particles in Brownian movement are used in the calculation of the range a virus-containing mucosal vary droplet can reach. Moreover, we used datas recorded in a previous paper named “Visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets” by B. E. Scharfman et. all to generate our results.

Forces in Schwarzschild, Vaidya and generalized Vaidya spacetimes

In this paper we investigate how the leading term in the geodesic equation in Schwarzschild spacetime changes under the coordinate transformation to Eddington-Finkelstein coordinates. This term corresponds to the Newton force of attraction. Also we consider this term when we add the energy-momentum tensor of the form of the null dust and the null perfect fluid into right-hand side of the Einstein equation. We estimate the value of this force in Vaidya spacetime when the naked singularity formation occurs. Also we give conditions in generalized Vaidya spacetime when this force of attraction is replaced by the force of repulsion.

Errors Related to General Relativity, Repulsive Gravitation and the Question of Black Holes

Galileo and Newton considered gravity to be independent of temperature, while Einstein claimed that the weight of metal will increase as temperature increases. Further, Maxwell maintained that charge is unrelated to gravity. Experiments show, however, that the weight of a metal piece is reduced as its temperature increases. Thus, charge-initiated repulsive gravitation exists. In fact, repulsive gravity has been demonstrated by the use of a charged capacitor hovering over Earth. Further, it is expected that a piece of heated metal would fall more slowly than a feather in a vacuum. Einstein developed an invalid notion of gravitational mass, and failed to establish the unification of gravitation and electromagnetism since he overlooked repulsive gravitation. Moreover, photons are a combination of the gravitational wave and the electromagnetic wave. For electromagnetic energy is invalid, and is in conflict with the Einstein equation. The non-linear Einstein equation has no bounded dynamic solution, Space-time singularity theorems are based on an invalid implicit assumption that all the couplings have a unique sign. Since gravity is no longer always attractive, the existence of black holes is questionable. The fact that Penrose was awarded the 2020 Nobel Prize in Physics for the derivation of black holes is due to that the Nobel Prize Committee for Physics did not sufficiently understand the physics of general relativity. A distinct characteristic of Penrose's work, as usual, is that it is not verifiable.

Existence and Uniqueness of Solutions of the Semiclassical Einstein Equation in Cosmological Models

We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical approximation, the backreaction of matter to curvature is taken into account by equating the Einstein tensor to the expectation values of the stress-energy tensor in a suitable state. We impose initial conditions for the scale factor at finite time, and we show that a regular state for the quantum matter compatible with these initial conditions can be chosen. Contributions with derivative of the coefficient of the metric higher than the second are present in the expectation values of the stress-energy tensor and the term with the highest derivative appears in a non-local form. This fact forbids a direct analysis of the semiclassical equation, and in particular, standard recursive approaches to approximate the solution fail to converge. In this paper, we show that, after partial integration of the semiclassical Einstein equation in cosmology, the non-local highest derivative appears in the expectation values of the stress-energy tensor through the application of a linear unbounded operator which does not depend on the details of the chosen state. We prove that an inversion formula for this operator can be found, furthermore, the inverse happens to be more regular than the direct operator and it has the form of a retarded product, hence, causality is respected. The found inversion formula applied to the traced Einstein equation has thus the form of a fixed point equation. The proof of local existence and uniqueness of the solution of the semiclassical Einstein equation is then obtained applying the Banach fixed point theorem.