Related papers: The Lense--Thirring Effect and Mach's Principle
We study the effect of the cosmological constant $\Lambda$ on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account,…
We interpret the well known fact that the equations for light rays in the Kottler or Schwarzschild-de Sitter metric are independent of the cosmological constant in terms of the projective equivalence of the optical metric for any value of…
It is known that the rotation of a gravitational lens affects properties of images. We consider an inverse problem: If the lens is dark, can we infer its rotation from the observed images? We find that, up to the first order in the…
Rotation of a body, according to Einstein's theory of general relativity, generates a "force" on other matter; in Newton's gravitational theory only the mass of a body produces a force. This phenomenon, due to currents of mass, is known as…
Two recent articles by Norman H. March that contain misleading statements concerning 3D Ising models, partly based on earlier erroneous work of Z.D. Zhang, are addressed.
Various authors have investigated the problem of light deflection by radially moving gravitational lenses - with inconsistent results. In this paper we generalize the calculations for arbitrary lens velocities and show that, to first order…
We discuss how the Reissner-Mindlin plate model can be derived from three-dimensional finite elasticity in terms of $\Gamma$-convergence. The presence of transverse shear effects in the Reissner-Mindlin model requires to scale different…
The optical Magnus effect refers to transverse shift of a trajectory of light caused by its polarization and appears as a correction to geometrical optics at the linear order in wavelength. Here, we start from Maxwell's equations in a…
We study the non-equilibrium behavior of three-dimensional spin glasses in the Migdal-Kadanoff approximation, that is on a hierarchical lattice. In this approximation the model has an unique ground state and equilibrium properties correctly…
As gravitational lensing measurements become increasingly precise, it becomes necessary to include ever higher order effects in the theoretical calculations. Here we show how the difference between the shear and the reduced shear manifest…
A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorenzian isometries of our new de Sitter relativity [I. I. Cot\u…
We developed a formula for the law of reflection of a plane-polarized light beam from an inclined flat mirror in uniform rectilinear motion by a direct application of the Huygens-Fresnel principle. Applying the obtained formula and the…
We summarize some critical issues pertaining the tests of the general relativistic Lense-Thirring effect performed by I. Ciufolini and coworkers in the gravitational field of the Earth with the geodetic satellites LAGEOS and LAGEOS II…
The bending of lightrays by the gravitational field of a ``lens'' that is moving relative to the observer is calculated within the approximation of weak fields, small angles and thin lenses. Up to first order in $v/c$ -- and assuming the…
Mach's principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach's principle in which matter and geometry are in one-to-one correspondence. Einstein's equations are not…
We study sigma-ideals and regularity properties related to the "filter-Laver" and "dual-filter-Laver" forcing partial orders. An important innovation which enables this study is a dichotomy theorem proved recently by Miller [1]. [1] Arnold…
Frank Wilczek's essay "Total Relativity: Mach 2004" (PHYSICS TODAY April, 2004, p. 10) cogently updates the status of the intuitively compelling, but partly unrealized, theory of Mach's Principle. I think, however, that an important…
In the literature, there is no consensus on the origin of the relativistic Sagnac effect, particularly from the standpoint of the rotating observer. The experiments of Wang et al. \cite{wang2003modified,wang2004generalized} has, however,…
Starting from an $n$-point circular gravitational lens having $3n+1$ images, Rhie (2003) used a perturbation argument to construct an $(n+1)$-point lens producing $5n$ images. In this work we give a concise proof of Rhie's result, and we…
In this letter we further analyze the concept of the use of a pair of identical geodetic satellites placed in identical orbits except for the inclinations which should be supplementary for measuring the Lense-Thirring effect in the…