4,949 research outputs found
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 -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
, 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
to which the particles equilibrate obeys a generalized equipartition
relation, in which the associated thermal energy 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 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
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