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

Estimating the final spin of a binary black hole coalescence

We present a straightforward approach for estimating the final black hole spin of a binary black hole coalescence with arbitrary initial masses and spins. Making some simple assumptions, we estimate the final angular momentum to be the sum of the individual spins plus the orbital angular momentum of a test particle orbiting at the last stable orbit around a Kerr black hole with a spin parameter of the final black hole. The formula we obtain is able to reproduce with reasonable accuracy the results from available numerical simulations, but, more importantly, it can be used to investigate what configurations might give rise to interesting dynamics. In particular, we discuss scenarios which might give rise to a ``flip'' in the direction of the total angular momentum of the system. By studying the dependence of the final spin upon the mass ratio and initial spins we find that our simple approach suggests that it is not possible to spin-up a black hole to extremal values through merger scenarios irrespective of the mass ratio of the objects involved.Comment: 9 pages, 8 figure

On the stable configuration of ultra-relativistic material spheres. The solution for the extremely hot gas

During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a positive-valued energy to balance the decrease. We derive the internal-state properties of the ideal gas situated in an extremely strong, ultra-relativistic gravitational field and suggest to apply our result to a compact object with the radius which is slightly larger than or equal to the Schwarzschild's gravitational radius. On the surface of the object, we find that the extreme attractivity of the gravity is accompanied with an extremely high internal, heat energy. This internal energy implies a correspondingly high pressure, the gradient of which has such a behavior that it can compete with the gravity. In a more detail, we find the equation of state in the case when the magnitude of the potential-type energy of constituting gas particles is much larger than their rest energy. This equation appears to be identical with the general-relativity condition of the equilibrium between the gravity and pressure gradient. The consequences of the identity are discussed.Comment: 12 pages (no figure, no table) Changes in 3-rd version: added an estimate of neutrino cooling and relative time-scale of the final stage of URMS collaps

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 transition from adiabatic inspiral to geodesic plunge for a compact object around a massive Kerr black hole: Generic orbits

The inspiral of a stellar mass compact object falling into a massive Kerr black hole can be broken into three different regimes: An adiabatic inspiral phase, where the inspiral timescale is much larger than the orbital period; a late-time radial infall, which can be approximated as a plunging geodesic; and a regime where the body transitions from the inspiral to plunge. In earlier work, Ori and Thorne have outlined a method to compute the trajectory during this transition for a compact object in a circular, equatorial orbit. We generalize this technique to include inclination and eccentricity.Comment: 11 pages, 6 figures. Accepted by Phys. Rev. D. New version addresses referee's comment

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

Hexagonal convection patterns in atomistically simulated fluids

Molecular dynamics simulation has been used to model pattern formation in three-dimensional Rayleigh--Benard convection at the discrete-particle level. Two examples are considered, one in which an almost perfect array of hexagonally-shaped convection rolls appears, the other a much narrower system that forms a set of linear rolls; both pattern types are familiar from experiment. The nature of the flow within the convection cells and quantitative aspects of the development of the hexagonal planform based on automated polygon subdivision are analyzed. Despite the microscopic scale of the system, relatively large simulations with several million particles and integration timesteps are involved.Comment: 4 pages, 6 figures (color figures have low resolution, high resolution figures available on author's website) Minor changes to text. To appear in PRE (Rapid Comm

Paradox of inductionless magnetorotational instability in a Taylor-Couette flow with a helical magnetic field

We consider the magnetorotational instability (MRI) of a hydrodynamically stable Taylor-Couette flow with a helical external magnetic field in the inductionless approximation defined by a zero magnetic Prandtl number (\Pm=0). This leads to a considerable simplification of the problem eventually containing only hydrodynamic variables. First, we point out that the energy of any perturbation growing in the presence of magnetic field has to grow faster without the field. This is a paradox because the base flow is stable without the magnetic while it is unstable in the presence of a helical magnetic field without being modified by the latter as it has been found recently by Hollerbach and Rudiger [Phys. Rev. Lett. 95, 124501 (2005)]. We revisit this problem by using a Chebyshev collocation method to calculate the eigenvalue spectrum of the linearized problem. In this way, we confirm that MRI with helical magnetic field indeed works in the inductionless limit where the destabilization effect appears as an effective shift of the Rayleigh line. Second, we integrate the linearized equations in time to study the transient behavior of small amplitude perturbations, thus showing that the energy arguments are correct as well. However, there is no real contradiction between both facts. The linear stability theory predicts the asymptotic development of an arbitrary small-amplitude perturbation, while the energy stability theory yields the instant growth rate of any particular perturbation, but it does not account for the evolution of this perturbation.Comment: 4 pages, 3 figures, submitted to Phys. Rev.

Asymptotic Quasinormal Frequencies of Different Spin Fields in Spherically Symmetric Black Holes

We consider the asymptotic quasinormal frequencies of various spin fields in Schwarzschild and Reissner-Nordstr\"om black holes. In the Schwarzschild case, the real part of the asymptotic frequency is ln3 for the spin 0 and the spin 2 fields, while for the spin 1/2, the spin 1, and the spin 3/2 fields it is zero. For the non-extreme charged black holes, the spin 3/2 Rarita-Schwinger field has the same asymptotic frequency as that of the integral spin fields. However, the asymptotic frequency of the Dirac field is different, and its real part is zero. For the extremal case, which is relevant to the supersymmetric consideration, all the spin fields have the same asymptotic frequency, the real part of which is zero. For the imaginary parts of the asymptotic frequencies, it is interesting to see that it has a universal spacing of $1/4M$ for all the spin fields in the single-horizon cases of the Schwarzschild and the extreme Reissner-Nordstr\"om black holes. The implications of these results to the universality of the asymptotic quasinormal frequencies are discussed.Comment: Revtex, 17 pages, 3 eps figures; one table, some remarks and references added to section I