Collisions of rigidly rotating disks of dust in General Relativity

We discuss inelastic collisions of two rotating disks by using the conservation laws for baryonic mass and angular momentum. In particular, we formulate conditions for the formation of a new disk after the collision and calculate the total energy loss to obtain upper limits for the emitted gravitational energy.Comment: 30 pages, 9 figure

Non-existence of stationary two-black-hole configurations: The degenerate case

In a preceding paper we examined the question whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. Based on the solution of a boundary value problem for two separate (Killing-) horizons and a novel black hole criterion we were able to prove the non-existence of the equilibrium configuration in question. In this paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 figure

Spin-Orbit Coupling and the Evolution of Transverse Spin

We investigate the evolution of transverse spin in tightly focused circularly polarized beams of light, where spin-orbit coupling causes a local rotation of the polarization ellipses upon propagation through the focal volume. The effect can be explained as a relative Gouy-phase shift between the circularly polarized transverse field and the longitudinal field carrying orbital angular momentum. The corresponding rotation of the electric transverse spin density is observed experimentally by utilizing a recently developed reconstruction scheme, which relies on transverse-spin-dependent directional scattering of a nano-probe.Comment: 4 pages, 2 figure

The interior of axisymmetric and stationary black holes: Numerical and analytical studies

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms of a single-domain fully pseudo-spectral scheme. Thereafter, a rigorous mathematical approach is given, in which soliton methods are utilized to derive an explicit relation between the event horizon and an inner Cauchy horizon. This horizon arises as the boundary of the future domain of dependence of the event horizon. Our numerical studies provide strong evidence for the validity of the universal relation \Ap\Am = (8\pi J)^2 where \Ap and \Am are the areas of event and inner Cauchy horizon respectively, and $J$ denotes the angular momentum. With our analytical considerations we are able to prove this relation rigorously.Comment: Proceedings of the Spanish Relativity Meeting ERE 2010, 10 pages, 5 figure

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

Stability of general relativistic Miyamoto-Nagai galaxies

The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well known Miyamoto-Nagai model that represents well a thick galactic disk. The stability of the disk is investigated under a general first order perturbation keeping the spacetime metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disk. We have that flat galaxies have more not-stable modes than the thick ones i.e., flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms.Comment: 11 pages, 5 figures, accepted for publication in MNRA

Relativistic Models of Galaxies

A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model three-dimensional distributions of matter in galaxies. The components of the energy-momentum tensor are calculated for the first two Miyamoto-Nagai potentials and a particular potential due to Satoh. The three potentials yield distributions of matter in which all tensions are pressures and all energy conditions are satisfied for certain ranges of the free parameters. A few non-planar geodesic orbits are computed for one of the potentials and compared with the Newtonian case. Rotation is also incorporated to the models and the effects of the source rotation on the rotation profile are calculated as first order corrections by using an approximate form of the Kerr metric in isotropic coordinates.Comment: 18 pages, 23 eps figures, uses mn2e.cls style file, to be published in MNRA

Clean and As-covered zinc-blende GaN (001) surfaces: Novel surface structures and surfactant behavior

We have investigated clean and As-covered zinc-blende GaN (001) surfaces, employing first-principles total-energy calculations. For clean GaN surfaces our results reveal a novel surface structure very different from the well-established dimer structures commonly observed on polar III-V (001) surfaces: The energetically most stable surface is achieved by a Peierls distortion of the truncated (1x1) surface rather than through addition or removal of atoms. This surface exhibits a (1x4) reconstruction consisting of linear Ga tetramers. Furthermore, we find that a submonolayer of arsenic significantly lowers the surface energy indicating that As may be a good surfactant. Analyzing surface energies and band structures we identify the mechanisms which govern these unusual structures and discuss how they might affect growth properties.Comment: 4 pages, 3 figures, to be published in Appears in Phys. Rev. Lett. (in print). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

A Luminous Companion to SGR 1806-20

We have obtained infrared spectra of the star suggested to be the counterpart of the soft gamma-ray repeater (SGR) 1806-20. We found strong emission lines similar to those seen in the spectra of the rare Luminous Blue Variables and B[e] stars. A He I absorption line is also seen, from which we infer a spectral type O9--B2. This classification, in combination with the minimum distance of \simgt6 kpc inferred from its extinction, makes the star one of the most luminous in the Galaxy. We infer that it is a companion to SGR 1806-20, and suggest that the presence of a companion is somehow related to the SGR phenomenon.Comment: 5 pages, AASTEX text+table and 2 PostScript figures (needs LaTeX style files aaspptwo.sty, epsf.sty and rotate.sty). In case of problems, contact [email protected]. Postscript file of complete article available on request. (Replaced because first version had one wrong reference in it