Related papers: Schwarzschild solution and Mach's principle
The double Schwarzschild solution in the equal mass case is studied in bispherical coordinates. An explicit conformal transformation from cylindrical Weyl coordinates to bispherical coordinates is given in terms of elliptic functions. A…
It has been thirty years since the discovery of the Unruh effect. It has played a crucial role in our understanding that the particle content of a field theory is observer dependent. This effect is important in its own right and as a way to…
Through an analysis and a generalization of a profound Fock's treatment, I make conspicuous the physically essential role of those functions of the polar radial coordinate for which the expressions of the spacetime interval are everywhere…
The deep reason why the equations describing axial and polar perturbations of Schwarzschild black holes have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on…
The purpose of this article is to introduce and study a relativistic motion whose acceleration, in proper time, is given by a white noise. We deal with general relativity, and consider more closely the problem of the asymptotic behaviour of…
Approximative analytic solutions of the Dirac equation in the geometry of Schwarzschild black holes are derived obtaining information about the discrete energy levels and the asymptotic behavior of the energy eigenspinors.
The Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in linear approximation. We present its exact solutions in terms of the confluent Heun's functions, the basic properties of the general solution, novel…
Order parameter equations, such as the complex Swift-Hohenberg (CSH) equation, offer a simplified and universal description that hold close to an instability threshold. The universality of the description refers to the fact that the same…
Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry.…
An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
We respond to a recent paper by Rindler on the ``Anti--Machian'' nature of the Lense--Thirring effect. We remark that his conclusion depends crucially on the particular formulation of Mach's principle used.
It was suggested by Unruh that a uniformly accelerated detector in vacuum would perceive a noise with a thermal distribution. We obtain a representation of solutions of the wave equation in two dimensions suitable for the Rindler regions.…
Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…
We introduce a method to compute particle detector transition probability in spacetime regions of general curved spacetimes provided that the curvature is not above a maximum threshold. In particular we use this method to compare the…
This paper has been withdrawn by the author due to the triviality of the considered coordinate transformations. A consistent treatment, based on the extended physical radial coordinate, is presented in the publications of the author 2000 -…
Tetrad field, with two unknown functions of radial coordinate and an angle $\Phi$ which is the polar angle $\phi$ times a function of the redial coordinate, is applied to the field equation of modified theory of gravity. Exact vacuum…
A study of the spin 1 Unruh-De Witt detectors interacting with a relativistic scalar quantum field is presented. After tracing out the field modes, the resulting density matrix for a bipartite qutrit system is employed to investigate the…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…