9,133 research outputs found
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
The evolution of the color gradients of early-type cluster galaxies
We investigate the origin of color gradients in cluster early-type galaxies
to probe whether pure age or pure metallicity gradients can explain the
observed data in local and distant (z approx 0.4) samples. We measure the
surface brightness profiles of the 20 brightest early-type galaxies of
CL0949+44 (hereafter CL0949) at redshift z=0.35-0.38 from HST WF2 frames taken
in the filters F555W, F675W, F814W. We determine the color profiles (V-R)(r),
(V-I)(r), and (R-I)(r) as a function of the radial distance r in arcsec, and
fit logarithmic gradients in the range -0.2 to 0.1 mag per decade. These values
are similar to what is found locally for the colors (U-B), (U-V), (B-V) which
approximately match the (V-R), (V-I), (R-I) at redshift approx 0.4. We analyse
the results with up to date stellar population models. We find that passive
evolution of metallicity gradients (approx 0.2 dex per radial decade) provides
a consistent explanation of the local and distant galaxies' data. Invoking pure
age gradients (with fixed metallicity) to explain local color gradients
produces too steep gradients at redshifts z approx 0.4. Pure age gradients are
consistent with the data only if large present day ages (>=15 Gyr) are assumed
for the galaxy centers.Comment: 23 pages, 19 figures, Accepted for publication in A&
Prospects for direct detection of circular polarization of gravitational-wave background
We discussed prospects for directly detecting circular polarization signal of
gravitational wave background. We found it is generally difficult to probe the
monopole mode of the signal due to broad directivity of gravitational wave
detectors. But the dipole (l=1) and octupole (l=3) modes of the signal can be
measured in a simple manner by combining outputs of two unaligned detectors,
and we can dig them deeply under confusion and detector noises. Around f~0.1mHz
LISA will provide ideal data streams to detect these anisotropic components
whose magnitudes are as small as ~1 percent of the detector noise level in
terms of the non-dimensional energy density \Omega_{GW}(f).Comment: 5 pages, 1 figure, PRL in pres
Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction
The next-to-leading term of the renormalized stress-energy tensor of the
quantized massive field with an arbitrary curvature coupling in the spacetime
of the Schwarzschild black hole is constructed. It is achieved by functional
differentiation of the DeWitt-Schwinger effective action involving coincidence
limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients and
The back reaction of the quantized field upon the Schwarzschild black
hole is briefly discussed
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions
We construct approximate initial data for non-spinning black hole binary
systems by asymptotically matching the 4-metrics of two tidally perturbed
Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian
4-metric in ADMTT coordinates. The specific matching procedure used here
closely follows the calculation in gr-qc/0503011, and is performed in the so
called buffer zone where both the post-Newtonian and the perturbed
Schwarzschild approximations hold. The result is that both metrics agree in the
buffer zone, up to the errors in the approximations. However, since isotropic
coordinates are very similar to ADMTT coordinates, matching yields better
results than in the previous calculation, where harmonic coordinates were used
for the post-Newtonian 4-metric. In particular, not only does matching improve
in the buffer zone, but due to the similarity between ADMTT and isotropic
coordinates the two metrics are also close to each other near the black hole
horizons. With the help of a transition function we also obtain a global smooth
4-metric which has errors on the order of the error introduced by the more
accurate of the two approximations we match. This global smoothed out 4-metric
is obtained in ADMTT coordinates which are not horizon penetrating. In
addition, we construct a further coordinate transformation that takes the
4-metric from global ADMTT coordinates to new coordinates which are similar to
Kerr-Schild coordinates near each black hole, but which remain ADMTT further
away from the black holes. These new coordinates are horizon penetrating and
lead, for example, to a lapse which is everywhere positive on the t=0 slice.
Such coordinates may be more useful in numerical simulations.Comment: 25 pages, 21 figures. Replaced with accepted versio
PT-symmetry breaking in complex nonlinear wave equations and their deformations
We investigate complex versions of the Korteweg-deVries equations and an Ito
type nonlinear system with two coupled nonlinear fields. We systematically
construct rational, trigonometric/hyperbolic, elliptic and soliton solutions
for these models and focus in particular on physically feasible systems, that
is those with real energies. The reality of the energy is usually attributed to
different realisations of an antilinear symmetry, as for instance PT-symmetry.
It is shown that the symmetry can be spontaneously broken in two alternative
ways either by specific choices of the domain or by manipulating the parameters
in the solutions of the model, thus leading to complex energies. Surprisingly
the reality of the energies can be regained in some cases by a further breaking
of the symmetry on the level of the Hamiltonian. In many examples some of the
fixed points in the complex solution for the field undergo a Hopf bifurcation
in the PT-symmetry breaking process. By employing several different variants of
the symmetries we propose many classes of new invariant extensions of these
models and study their properties. The reduction of some of these models yields
complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv
policy; higher resolutions maybe obtained from the authors upon request
- …