5,750 research outputs found
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
Dipole Perturbations of the Reissner-Nordstrom Solution: The Polar Case
The formalism developed by Chandrasekhar for the linear polar perturbations
of the Reissner-Nordstrom solution is generalized to include the case of dipole
(l=1) perturbations. Then, the perturbed metric coefficients and components of
the Maxwell tensor are computed.Comment: 16 pages, LaTeX, no figures. Submitted for publication in Physical
Review
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
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
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
Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
A black hole casts a shadow as an optical appearance because of its strong
gravitational field. We study how to determine the spin parameter and the
inclination angle by observing the apparent shape of the shadow, which is
distorted mainly by those two parameters. Defining some observables
characterizing the apparent shape (its radius and distortion parameter), we
find that the spin parameter and inclination angle of a Kerr black hole can be
determined by the observation. This technique is also extended to the case of a
Kerr naked singularity.Comment: 9 pages, 11 figures; v2: references added, typos corrected; v3:
accepted for publication in Physical Review
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%
Anisotropy in Homogeneous Rotating Turbulence
The effective stress tensor of a homogeneous turbulent rotating fluid is
anisotropic. This leads us to consider the most general axisymmetric four-rank
``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent
effective force on large scales that arise from it, in addition to the
microscopic viscous force. Some of these terms involve couplings to vorticity
and others are angular momentum non conserving (in the rotating frame).
Furthermore, we explore the constraints on the response function and the
two-point velocity correlation due to axisymmetry. Finally, we compare our
viscosity tensor with other four-rank tensors defined in current approaches to
non-rotating anisotropic turbulence.Comment: 14 pages, RevTe
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
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
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