Related papers: Interpreting a conformally flat pure radiation spa…
We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime.…
As predicted by A. Einstein [Ann. Phys. (Leipzig) 17, 891 (1905)], the electromagnetic wave reflected at a moving mirror is frequency-upshifted and intensified as high as the mirror velocity is close to the speed of light in vacuum.…
In this article we consider large energy wave maps in dimension 2+1, as in the resolution of the threshold conjecture by Sterbenz and Tataru, but more specifically into the unit Euclidean sphere, and study further the dynamics of the…
We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her…
We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature…
Observing the list of compatible second order equations of Absolute Parallelism (AP) found by Einstein and Mayer (they used D=4), we choose the one-parameter class of equations which take on a 3-linear form (when contra-frame density of…
From a columnar approximation of the Euler equations of an incompressible fluid with surface tension, we derive in the short-wave approximation a new integrable classical 1+1 dimensional field theory for the motion of the surface. Together…
We point out that the (pseudo-)conformal Universe scenario may be realized as decay of conformally invariant, metastable vacuum, which proceeds via spontaneous nucleation and subsequent growth of a bubble of a putative new phase. We study…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
The collapse scenario of a scalar field along with a perfect fluid distribution is investigated for a conformally flat spacetime. The theorem for the integrability of an anharmonic oscillator has been utilized. For a pure power law…
A class of radiative solutions of Einstein's field equations with a negative cosmological constant and a pure radiation is investigated. The space-times, which generalize the Defrise solution, represent exact gravitational waves which…
The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen…
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis…
It is shown that a superconformal surface with arbitrary codimension in flat Euclidean space has a (necessarily unique) dual superconformal surface if and only if the surface is S-Willmore, the latter a well-known necessary condition to…
The propagation of plane electromagnetic waves in the gravitational field inside a rotating cloud of dark matter is analyzed. Formulas for the deflection and absorption of light, and the rotation of the polarization plane are obtained in…
A special-relativistic scalar-vector theory of gravitation is presented which mimics an important class of solutions of Einstein's gravitational field equations. The theory includes solutions equivalent to Schwarzschild, Kerr,…
It was shown long ago by T. V. Ruzmaikina and A. A. Ruzmaikin that within the framework of a homogeneous and isotropic cosmological model quadratic corrections of the gravitational field cannot provide solutions that are both regular…
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic…
The effects of the de Broglie-Bohm quantum potential on a test particle of mass $m$ are investigated in a conformally-flat geometry. A real, nonlinear, scalar field $\Psi$ is introduced and related directly to the conformal factor and to…