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 $D\le1$. 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 $a_{3}$ and $a_{4}.$ 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 $u_t+uu_x=0$, 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, $u_t-iu(iu_x)^\epsilon= 0$ ($\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\epsilon$ 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