Non-Supersymmetric Attractors in BI black holes

We study attractor mechanism in extremal black holes of Einstein-Born-Infeld theories in four dimensions. We look for solutions which are regular near the horizon and show that they exist and enjoy the attractor behavior. The attractor point is determined by extremization of the effective potential at the horizon. This analysis includes the backreaction and supports the validity of non-supersymmetric attractors in the presence of higher derivative interactions in the gauge field part.Comment: 15 pages, minor corrections, references adde

Electrodynamics in Friedmann-Robertson-Walker Universe: Maxwell and Dirac fields in Newman-Penrose formalism

Maxwell and Dirac fields in Friedmann-Robertson-Walker spacetime is investigated using the Newman-Penrose method. The variables are all separable, with the angular dependence given by the spin-weighted spherical harmonics. All the radial parts reduce to the barrier penetration problem, with mostly repulsive potentials representing the centrifugal energies. Both the helicity states of the photon field see the same potential, but that of the Dirac field see different ones; one component even sees attractive potential in the open universe. The massless fields have the usual exponential time dependencies; that of the massive Dirac field is coupled to the evolution of the cosmic scale factor $a$. The case of the radiation filled flat universe is solved in terms of the Whittaker function. A formal series solution, valid in any FRW universe, is also presented. The energy density of the Maxwell field is explicitly shown to scale as $a^{-4}$. The co-moving particle number density of the massless Dirac field is found to be conserved, but that of the massive one is not. Particles flow out of certain regions, and into others, creating regions that are depleted of certain linear and angular momenta states, and others with excess. Such current of charged particles would constitute an electric current that could generate a cosmic magnetic field. In contrast, the energy density of these massive particles still scales as $a^{-4}$.Comment: 18 pages including 9 figure

Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases

We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We establish that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature $T$, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics--they need not be in a state of thermal equilibrium. The temperature $T$ to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy $k_{\mathrm B}T$ is equal to an appropriately defined average of the scatterers' kinetic energy. In the equilibrated state, particle motion is diffusive

Dynamics of electromagnetic waves in Kerr geometry

Here we are interested to study the spin-1 particle i.e., electro-magnetic wave in curved space-time, say around black hole. After separating the equations into radial and angular parts, writing them according to the black hole geometry, say, Kerr black hole we solve them analytically. Finally we produce complete solution of the spin-1 particles around a rotating black hole namely in Kerr geometry. Obviously there is coupling between spin of the electro-magnetic wave and that of black hole when particles propagate in that space-time. So the solution will be depending on that coupling strength. This solution may be useful to study different other problems where the analytical results are needed. Also the results may be useful in some astrophysical contexts.Comment: 15 Latex pages, 4 Figures; Accepted for publication in Classical and Quantum Gravit

Non-stationary de Sitter cosmological models

In this note it is proposed a class of non-stationary de Sitter, rotating and non-rotating, solutions of Einstein's field equations with a cosmological term of variable function.Comment: 11 pages, Latex. International Journal of Modern Physics D (accepted for publication

Last scattering, relic gravitons and the circular polarization of the CMB

The tensor contribution to the $V$-mode polarization induced by a magnetized plasma at last scattering vanishes exactly. Conversely a polarized background of relic gravitons cannot generate a $V$-mode polarization. The reported results suggest that, in the magnetized $\Lambda$CDM paradigm, the dominant source of circular dichroism stems from the large-scale fluctuations of the spatial curvature.Comment: 8 pages, no figure

Hairy Black Holes and Null Circular Geodesics

Einstein-matter theories in which hairy black-hole configurations have been found are studied. We prove that the nontrivial behavior of the hair must extend beyond the null circular orbit (the photonsphere) of the corresponding spacetime. We further conjecture that the region above the photonsphere contains at least 50% of the total hair's mass. We support this conjecture with analytical and numerical results.Comment: 5 page

Behaviour of spin-1/2 particle around a charged black hole

Dirac equation is separable in curved space-time and its solution was found for both spherically and axially symmetric geometry. But most of the works were done without considering the charge of the black hole. Here we consider the spherically symmetric charged black hole background namely Reissner-Nordstrom black hole. Due to presence of the charge of black-hole charge-charge interaction will be important for the cases of incoming charged particle (e.g. electron, proton etc.). Therefore both gravitational and electromagnetic gauge fields should be introduced. Naturally behaviour of the particle will be changed from that in Schwarzschild geometry. We compare both the solutions. In the case of Reissner-Nordstrom black hole there is a possibility of super-radiance unlike Schwarzschild case. We also check this branch of the solution.Comment: 8 Latex pages and 4 Figures; RevTex.style; Accepted for Publication in Classical and Quantum Gravit

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

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk and it may be possible to access a turbulent regime in which many modes are unstable.Comment: 4 pages, 4 figures, to be published in Physical Review Letter