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

Colliding Plane Impulsive Gravitational Waves

When two non-interacting plane impulsive gravitational waves undergo a head-on collision, the vacuum interaction region between the waves after the collision contains backscattered gravitational radiation from both waves. The two systems of backscattered waves have each got a family of rays (null geodesics) associated with them. We demonstrate that if it is assumed that a parameter exists along each of these families of rays such that the modulus of the complex shear of each is equal then Einstein's vacuum field equations, with the appropriate boundary conditions, can be integrated systematically to reveal the well-known solutions in the interaction region. In so doing the mystery behind the origin of such solutions is removed. With the use of the field equations it is suggested that the assumption leading to their integration may be interpreted physically as implying that the energy densities of the two backscattered radiation fields are equal. With the use of different boundary conditions this approach can lead to new collision solutions.Comment: 21 pages, LaTeX2

Applied constant gain amplification in circulating loop experiments

The reconfiguration of channel or wavelength routes in optically transparent mesh networks can lead to deviations in channel power that may impact transmission performance. A new experimental approach, applied constant gain, is used to maintain constant gain in a circulating loop enabling the study of gain error effects on long-haul transmission under reconfigured channel loading. Using this technique we examine a number of channel configurations and system tuning operations for both full-span dispersion-compensated and optimized dispersion-managed systems. For each system design, large power divergence was observed with a maximum of 15 dB at 2240 km, when switching was implemented without additional system tuning. For a bit error rate of 10-3, the maximum number of loop circulations was reduced by up to 33%

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

Dynamic circulating-loop methods for transmission experiments in optically transparent networks

Recent experiments incorporating multiple fast switching elements and automated system configuration in a circulating loop apparatus have enabled the study of aspects of long-haul WDM transmission unique to optically transparent networks. Techniques include per-span switching to measure the performance limits due to dispersion compensation granularity and mesh network walk-off, and applied constant-gain amplification to evaluate wavelength reconfiguration penalties

Stellar Dynamics and Black Holes

Chandrasekhar's most important contribution to stellar dynamics was the concept of dynamical friction. I briefly review that work, then discuss some implications of Chandrasekhar's theory of gravitational encounters for motion in galactic nuclei.Comment: Talk presented at the "Chandrasekhar Centenary Conference" (2010

κ\kappa-Minkowski and Snyder algebra from reparametrisation symmetry

Following our earlier work \cite{sunandan1, sunandan2}, we derive noncommuting phase-space structures which are combinations of both the $\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation symmetry of the recently proposed Lagrangian for a point particle \cite{subir} satisfying the exact Doubly Special Relativity dispersion relation in the Magueijo-Smolin framework.Comment: Accepted in Euro Physics Letter

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure

Electron-Neutrino Bremsstrahlung in Electro-Weak Theory

The electron-neutrino bremsstrahlung process has been considered in the framework of electro-weak theory. The scattering cross section has been calculated in the center of mass frame and approximated to extreme relativistic as well as non-relativistic case. The rate of energy-loss via this type of bremsstrahlung process has been obtained both in non-degenerate and degenerate region. The effect of this electron-neutrino bremsstrahlung process in different ranges of temperature and density characterizing the late stages of stellar evolution has been discussed. It is found from our study that this bremsstrahlung process is highly important in the non-degenerate region, although it might have some significant effect in the extreme relativistic degenerate region.Comment: 18 pages including 4 figures and 1 table; Published in J. Phys

Exact Results for Evaporating Black Holes in Curvature-Squared Lovelock Gravity: Gauss-Bonnet Greybody Factors

Lovelock gravity is an important extension of General Relativity that provides a promising framework to study curvature corrections to the Einstein action, while avoiding ghosts and keeping second order field equations. This paper derives the greybody factors for D-dimensional black holes arising in a theory with a Gauss-Bonnet curvature-squared term. These factors describe the non-trivial coupling between black holes and quantum fields during the evaporation process: they can be used both from a theoretical viewpoint to investigate the intricate spacetime structure around such a black hole, and for phenomenological purposes in the framework of braneworld models with a low Planck scale. We derive exact spectra for the emission of scalar, fermion and gauge fields emitted on the brane, and for scalar fields emitted in the bulk, and demonstrate how the Gauss-Bonnet term can change the bulk-to-brane emission rates ratio in favour of the bulk channel in particular frequency regimes.Comment: 29 pages, Latex file, 11 figures, Data files (greybody factors) available at http://lpsc.in2p3.fr/ams/greybody/, typos corrected, references added, version to appear in Phys. Rev.