On a Localized Riemannian Penrose Inequality

Consider a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary is the disjoint union of two pieces: the horizon boundary and the outer boundary, where the horizon boundary consists of the unique closed minimal surfaces in the manifold and the outer boundary is metrically a round sphere. We obtain an inequality relating the area of the horizon boundary to the area and the total mean curvature of the outer boundary. Such a manifold may be thought as a region, surrounding the outermost apparent horizons of black holes, in a time-symmetric slice of a space-time in the context of general relativity. The inequality we establish has close ties with the Riemannian Penrose Inequality, proved by Huisken and Ilmanen, and by Bray.Comment: 16 page

Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes

We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the first variation, with fixed angular momentum, of the area is zero and the second variation is positive definite evaluated at the extreme Kerr throat initial data. This indicates that the area of the extreme Kerr throat initial data is a minimum among this class of data. And hence the area of generic throat initial data is bounded from below by the angular momentum. Also, this result strongly suggests that the inequality between area and angular momentum holds for generic asymptotically flat axially symmetric black holes. As an application, we prove this inequality in the non trivial family of spinning Bowen-York initial data.Comment: 11 pages. Changes in presentation and typos correction

Einstein equations in the null quasi-spherical gauge

The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we describe the structure of timelike boundary conditions; the matching problem across null hypersurfaces; and the propagation of gravitational shocks.Comment: 12 pages, LaTeX (revtex, amssymb), revision 18 pages, contains expanded discussion and explanations, updated references, to appear in CQ

A Remark on Boundary Effects in Static Vacuum Initial Data sets

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that the boundary of (M, g) has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that the boundary has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the area and mean curvature of the boundary. Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit

Thermal emittance measurements of a cesium potassium antimonide photocathode

Thermal emittance measurements of a CsK2Sb photocathode at several laser wavelengths are presented. The emittance is obtained with a solenoid scan technique using a high voltage dc photoemission gun. The thermal emittance is 0.56+/-0.03 mm-mrad/mm(rms) at 532 nm wavelength. The results are compared with a simple photoemission model and found to be in a good agreement.Comment: APL 201

Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds

We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.Comment: 15 page

Late time behaviour of the maximal slicing of the Schwarzschild black hole

A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be evolved into a foliation of the $r>3m/2$-region of the spacetime by maximal surfaces with the requirement that time runs equally fast at both spatial ends of the manifold. This paper studies the behaviour of these slices in the limit as proper time-at-infinity becomes arbitrarily large and gives an analytic expression for the collapse of the lapse.Comment: 18 pages, Latex, no figure

Electronic states and optical properties of PbSe nanorods and nanowires

A theory of the electronic structure and excitonic absorption spectra of PbS and PbSe nanowires and nanorods in the framework of a four-band effective mass model is presented. Calculations conducted for PbSe show that dielectric contrast dramatically strengthens the exciton binding in narrow nanowires and nanorods. However, the self-interaction energies of the electron and hole nearly cancel the Coulomb binding, and as a result the optical absorption spectra are practically unaffected by the strong dielectric contrast between PbSe and the surrounding medium. Measurements of the size-dependent absorption spectra of colloidal PbSe nanorods are also presented. Using room-temperature energy-band parameters extracted from the optical spectra of spherical PbSe nanocrystals, the theory provides good quantitative agreement with the measured spectra.Comment: 35 pages, 12 figure

Solutions of special asymptotics to the Einstein constraint equations

We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.Comment: 13 pages; the error in Lemma 3.5 fixed and typos corrected; to appear in Class. Quantum Gra