7,704 research outputs found
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 . 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 . 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 .Comment: 18 pages including 9 figure
Perturbed Self-Similar Massless Scalar Field in Spherically Symmetric Spaceimes
In this paper, we investigate the linear perturbations of the spherically
symmetric spacetimes with kinematic self-similarity of the second kind. The
massless scalar field equations are solved which yield the background and an
exact solutions for the perturbed equations. We discuss the boundary conditions
of the resulting perturbed solutions. The possible perturbation modes turn out
to be stable as well as unstable. The analysis leads to the conclusion that
there does not exist any critical solution.Comment: 15 pages, accepted for publication Int. J. Mod. Phys.
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
Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability
We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability
using three-dimensional MHD simulations. We consider the idealized case of two
inviscid, perfectly conducting fluids of constant density separated by a
contact discontinuity perpendicular to the effective gravity g, with a uniform
magnetic field B parallel to the interface. Modes parallel to the field with
wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h
and d_l are the densities of the heavy and light fluids respectively), whereas
modes perpendicular to B are unaffected. We study strong fields with l_c
varying between 0.01 and 0.36 of the horizontal extent of the computational
domain. Even a weak field produces tension forces on small scales that are
significant enough to reduce shear (as measured by the distribution of the
amplitude of vorticity), which in turn reduces the mixing between fluids, and
increases the rate at which bubbles and finger are displaced from the interface
compared to the purely hydrodynamic case. For strong fields, the highly
anisotropic nature of unstable modes produces ropes and filaments. However, at
late time flow along field lines produces large scale bubbles. The kinetic and
magnetic energies transverse to gravity remain in rough equipartition and
increase as t^4 at early times. The growth deviates from this form once the
magnetic energy in the vertical field becomes larger than the energy in the
initial field. We comment on the implications of our results to Z-pinch
experiments, and a variety of astrophysical systems.Comment: 25 pages, accepted by Physics of Fluids, online version of journal
has high resolution figure
Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field
The Klein-Gordon and Dirac equations in a semi-infinite lab (), in the
background metric \ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2, are
investigated. The resulting equations are studied for the special case . It is shown that in the case of zero transverse-momentum, the square
of the energy eigenvalues of the spin-1/2 particles are less than the squares
of the corresponding eigenvalues of spin-0 particles with same masses, by an
amount of . Finally, for nonzero transverse-momentum, the energy
eigenvalues corresponding to large quantum numbers are obtained, and the
results for spin-0 and spin-1/2 particles are compared to each other.Comment: 12 pages, LaTeX 2
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 Pulsations excited by a scattered mass
We compute the energy spectra of the gravitational signals emitted when a
mass m is scattered by the gravitational field of a star of mass M >> m. We
show that, unlike black holes in similar processes, the quasi-normal modes of
the star are excited, and that the amount of energy emitted in these modes
depends on how close the exciting mass can get to the star.Comment: 23 pages, 6 figures, RevTe
The Effect of Sources on the Inner Horizon of Black Holes
Single pulse of null dust and colliding null dusts both transform a regular
horizon into a space-like singularity in the space of colliding waves. The
local isometry between such space-times and black holes extrapolates these
results to the realm of black holes. However, inclusion of particular scalar
fields instead of null dusts creates null singularities rather than space-like
ones on the inner horizons of black holes.Comment: Final version to appear in PR
Simple Waves in Ideal Radiation Hydrodynamics
In the dynamic diffusion limit of radiation hydrodynamics, advection
dominates diffusion; the latter primarily affects small scales and has
negligible impact on the large scale flow. The radiation can thus be accurately
regarded as an ideal fluid, i.e., radiative diffusion can be neglected along
with other forms of dissipation. This viewpoint is applied here to an analysis
of simple waves in an ideal radiating fluid. It is shown that much of the
hydrodynamic analysis carries over by simply replacing the material sound
speed, pressure and index with the values appropriate for a radiating fluid. A
complete analysis is performed for a centered rarefaction wave, and expressions
are provided for the Riemann invariants and characteristic curves of the
one-dimensional system of equations. The analytical solution is checked for
consistency against a finite difference numerical integration, and the validity
of neglecting the diffusion operator is demonstrated. An interesting physical
result is that for a material component with a large number of internal degrees
of freedom and an internal energy greater than that of the radiation, the sound
speed increases as the fluid is rarefied. These solutions are an excellent test
for radiation hydrodynamic codes operating in the dynamic diffusion regime. The
general approach may be useful in the development of Godunov numerical schemes
for radiation hydrodynamics.Comment: 16 pages, 10 figures, accepted for publication in The Astrophysical
Journa
Black hole quasinormal mode spectroscopy with LISA
The signal-to-noise ratio (SNR) for black hole quasinormal mode sources of
low-frequency gravitational waves is estimated using a Monte Carlo approach
that replaces the all-sky average approximation. We consider an eleven
dimensional parameter space that includes both source and detector parameters.
We find that in the black-hole mass range - the
SNR is significantly higher than the SNR for the all-sky average case, as a
result of the variation of the spin parameter of the sources. This increased
SNR may translate to a higher event rate for the Laser Interferometer Space
Antenna (LISA). We also study the directional dependence of the SNR, show at
which directions in the sky LISA will have greater response, and identify the
LISA blind spots.Comment: 12 pages, 5 figure
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