The influence of the precipitation rate on the properties of porous chromia

The properties were studied of heated (320°C) chromia samples, prepared by two precipitation methods: \ud \ud 1. (1) addition of ammonia to chromium salt solutions,\ud 2. (2) OH− formation in chromium salt solutions through hydrolysis of urea.\ud \ud Samples formed by means of the first method are macro or mesoporous and have a lower specific surface area (~200 m2·g−1) than those formed by urea hydrolysis (~300 m2·g−1). Only in the case of a very slow addition of the ammonia solution these properties of the chromia's become equal. Experiments show that the micro porous type samples with high surface area are only formed if the pH range 5.1 to 5.7 is passed slowly. The formation of polychromium complexes of uniform size is suggested.\ud \u

Gravitational radiation from dynamical black holes

An effective energy tensor for gravitational radiation is identified for uniformly expanding flows of the Hawking mass-energy. It appears in an energy conservation law expressing the change in mass due to the energy densities of matter and gravitational radiation, with respect to a Killing-like vector encoding a preferred flow of time outside a black hole. In a spin-coefficient formulation, the components of the effective energy tensor can be understood as the energy densities of ingoing and outgoing, transverse and longitudinal gravitational radiation. By anchoring the flow to the trapping horizon of a black hole in a given sequence of spatial hypersurfaces, there is a locally unique flow and a measure of gravitational radiation in the strong-field regime.Comment: 5 revtex4 pages. Additional comment

Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.Comment: RevTeX; 32 pp. Accepted by Phys. Rev. D. Added references and extra comments in introductio

First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models

We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a FLRW spacetime with arbitrary perturbations. The matching hypersurface is also perturbed arbitrarily and, in all cases, the perturbations are decomposed into scalars using the Hodge operator on the sphere. This allows us to write down the matching conditions in a compact way. In particular, we find that the existence of a perturbed (rotating, stationary and vacuum) Schwarzschild cavity in a perturbed FLRW universe forces the cosmological perturbations to satisfy constraints that link rotational and gravitational wave perturbations. We also prove that if the perturbation on the FLRW side vanishes identically, then the vacuole must be perturbatively static and hence Schwarzschild. By the dual nature of the problem, the first result translates into links between rotational and gravitational wave perturbations on a perturbed Oppenheimer-Snyder model, where the perturbed FLRW dust collapses in a perturbed Schwarzschild environment which rotates in equilibrium. The second result implies in particular that no region described by FLRW can be a source of the Kerr metric.Comment: LaTeX; 29 page

Local existence of dynamical and trapping horizons

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally outer trapped slices which lie in the leaves of the given foliation. We also show that under rather weak energy conditions this horizon must be either achronal or spacelike everywhere. Furthermore, we discuss the relation between ``bounding'' and ``stability'' properties of marginally outer trapped surfaces.Comment: 4 pages, 1 figure, minor change

Searching for thermal signatures of persistent currents in normal metal rings

We introduce a calorimetric approach to probe persistent currents in normal metal rings. The heat capacity of a large ensemble of silver rings is measured by nanocalorimetry under a varying magnetic field at different temperatures (60 mK, 100 mK and 150 mK). Periodic oscillations versus magnetic field are detected in the phase signal of the temperature oscillations, though not in the amplitude (both of them directly linked to the heat capacity). The period of these oscillations ($\Phi_0/2$, with $\Phi_0 = h/e$ the magnetic flux quantum) and their evolution with temperature are in agreement with theoretical predictions. In contrast, the amplitude of the corresponding heat capacity oscillations (several $k_{\mathrm{B}}$) is two orders of magnitude larger than predicted by theory

A counter-example to a recent version of the Penrose conjecture

By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.Comment: 12 pages. Appendix added with technical details. To appear in Classical and Quantum Gravit

First and Second Order Perturbations of Hypersurfaces

In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface $\Sigma$ in a spacetime $(M,g)$, when the metric $g$ is perturbed arbitrarily to second order and the hypersurface itself is allowed to change perturbatively (i.e. to move within spacetime) also to second order. The results are fully general and hold in arbitrary dimensions and signature. An application of these results for the perturbed matching theory between spacetimes is presented.Comment: 31 pages, no figures. To be published in Classical and Quantum Gravit