相关论文: Schwarzschild solution and Mach's principle
In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$) and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there is…
In this paper, we establish a boundary Schwarz lemma for solutions to non-homogeneous biharmonic equations.
The Schwarzschild black hole in the Cold Dark Matter (CDM) halo is studied, and the radiation laws of the thin accretion disk near the black hole are discussed and summarized. The orbits of light around the black hole are also calculated.…
In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in \cite{Yang} with a Sobolev embedding…
The multipole moments method is not only an aid to understand the deformation of the space-time, but also an effective tool to solve the approximate solutions of the Einstein field equation. However, The usual multipole moments are…
There is a persistent state of confusion regarding the nature of the Unruh effect. We will argue that, in contrast to some interpretations thereof, the effect does not represent any novel physics and that, by its very nature, the effect is…
The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work…
We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specializing to static fields with spherical symmetry, we obtain a second-order equation for one of the…
With the use of classical statistical argumentation similar to the one used in e.g. statistical optics, it is demonstrated that in entanglement of photons, a classical realist explanation cannot be excluded by the CHSH measure in…
We provide in this paper a first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime by using the conformal geometric approach. We will show that the existing decay results for the…
In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an…
A new representation for a regular solution of the radial Dirac system of a special form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with respect to the spectral parameter. For the…
The present work describes an immersion in 5D of the interior Schwarzschild solution of the general relativity equations. The model theory is defined in the context of a flat 5D space time matter Minkowski model, using a Tolman like…
The aim of these notes is to give a complete self-contained account of the current state of the art in the regularity for planar minimizers and critical points of the Mumford-Shah functional.
We review Unruh-DeWitt detectors and other models of detector-field interaction in a relativistic quantum field theory setting as a tool for extracting detector-detector, field-field and detector-field correlation functions of interest in…
We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and…
We consider the Bergman space on the complex plane. We prove an analogue of Schwarz's reflection principle for unbounded quasidisks.
It is well known that observers will be accelerated when they approach the planets. Thus, discussing the properties of accelerating observers in the Schwarzschild space is of sense. For the sake of simplicity, we can construct these…
We consider additive Schwarz methods for boundary value problems involving the $p$-Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for these methods, empirical evidence from numerical experiments…
This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using…