The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field of study. Extensions of the Bell-Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell-Szekeres solution is derived.Comment: 18 pages, Latex fil

The Effect of Sources on the Inner Horizon of Black Holes

Single pulse of null dust and colliding null dusts both transform a regular horizon into a space-like singularity in the space of colliding waves. The local isometry between such space-times and black holes extrapolates these results to the realm of black holes. However, inclusion of particular scalar fields instead of null dusts creates null singularities rather than space-like ones on the inner horizons of black holes.Comment: Final version to appear in PR

Second and higher-order perturbations of a spherical spacetime

The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.Comment: Accepted for publication in Physical Review

Thermal conductance of Andreev interferometers

We calculate the thermal conductance $G^T$ of diffusive Andreev interferometers, which are hybrid loops with one superconducting arm and one normal-metal arm. The presence of the superconductor suppresses $G^T$; however, unlike a conventional superconductor, $G^T/G^T_N$ does not vanish as the temperature $T\to0$, but saturates at a finite value that depends on the resistance of the normal-superconducting interfaces, and their distance from the path of the temperature gradient. The reduction of $G^T$ is determined primarily by the suppression of the density of states in the proximity-coupled normal metal along the path of the temperature gradient. $G^T$ is also a strongly nonlinear function of the thermal current, as found in recent experiments.Comment: 5 pages, 4 figure

On the stability of naked singularities

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition.Comment: 20 pages. 5 figure

The spatial correlations in the velocities arising from a random distribution of point vortices

This paper is devoted to a statistical analysis of the velocity fluctuations arising from a random distribution of point vortices in two-dimensional turbulence. Exact results are derived for the correlations in the velocities occurring at two points separated by an arbitrary distance. We find that the spatial correlation function decays extremely slowly with the distance. We discuss the analogy with the statistics of the gravitational field in stellar systems.Comment: 37 pages in RevTeX format (no figure); submitted to Physics of Fluid