Related papers: On the uniqueness of harmonic coordinates
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between…
A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d>3 such spacetimes are stable at both…
Unique features of particle orbits produce novel signatures of gravitational observable phenomena, and are quite useful in testing compact astrophysical objects in general relativity or modified theories of gravity. Here we observe a…
We consider dynamical spherically symmetric spacetimes, which are conformal to the static spherically symmetric metrics, and find new solutions of Einstein equations by symmetry considerations. Our study help us classify various conformal…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We extend earlier discussions of the balance problem for two black holes and study stationary spacetimes containing an arbitrary number of $n$ aligned rotating and (possibly) charged black holes. For these hypothetical equilibrium…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Some future global properties of cosmological solutions for the Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global existence is proved, the homogeneous spacetimes are future complete for causal trajectories, and the…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the…
We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary…
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…
Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy…
In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments, is studied. The condition on the multipole moments, for existence of a solution, is formulated as a convergence condition…
We study the behavior of static, spherically symmetric solutions to the field equations of scalar-tensor theories (STT) of gravity belonging to the Bergmann-Wagoner-Nordtvedt class, in the presence of an electric and/or magnetic charge.…
Symmetries compatible with asymptotic flatness and admitting gravitational and electromagnetic radiation are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in axially symmetric electrovacuum spacetimes in which at…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…
Vacuum 5-D Einstein equations with spherical symmetry and t-dependence are considered. For the case of separating variables several classes of exact solutions are obtained. Effective matter, induced by geometrical scalar field is analyzed.