Polymer state approximations of Schroedinger wave functions

It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum gravity.Comment: 11 pages, 1 figure, Conclusions section adde

Networks of gravitational wave detectors and three figures of merit

This paper develops a general framework for studying the effectiveness of networks of interferometric gravitational wave detectors and then uses it to show that enlarging the existing LIGO-VIRGO network with one or more planned or proposed detectors in Japan (LCGT), Australia, and India brings major benefits, including much larger detection rate increases than previously thought... I show that there is a universal probability distribution function (pdf) for detected SNR values, which implies that the most likely SNR value of the first detected event will be 1.26 times the search threshold. For binary systems, I also derive the universal pdf for detected values of the orbital inclination, taking into account the Malmquist bias; this implies that the number of gamma-ray bursts associated with detected binary coalescences should be 3.4 times larger than expected from just the beaming fraction of the gamma burst. Using network antenna patterns, I propose three figures of merit that characterize the relative performance of different networks... Adding {\em any} new site to the planned LIGO-VIRGO network can dramatically increase, by factors of 2 to 4, the detected event rate by allowing coherent data analysis to reduce the spurious instrumental coincident background. Moving one of the LIGO detectors to Australia additionally improves direction-finding by a factor of 4 or more. Adding LCGT to the original LIGO-VIRGO network not only improves direction-finding but will further increase the detection rate over the extra-site gain by factors of almost 2, partly by improving the network duty cycle... Enlarged advanced networks could look forward to detecting three to four hundred neutron star binary coalescences per year.Comment: 38 pages, 7 figures, 2 tables. Accepted for publication in Classical and Quantum Gravit

Horizon energy and angular momentum from a Hamiltonian perspective

Classical black holes and event horizons are highly non-local objects, defined in terms of the causal past of future null infinity. Alternative, (quasi)local definitions are often used in mathematical, quantum, and numerical relativity. These include apparent, trapping, isolated, and dynamical horizons, all of which are closely associated to two-surfaces of zero outward null expansion. In this paper we show that three-surfaces which can be foliated with such two-surfaces are suitable boundaries in both a quasilocal action and a phase space formulation of general relativity. The resulting formalism provides expressions for the quasilocal energy and angular momentum associated with the horizon. The values of the energy and angular momentum are in agreement with those derived from the isolated and dynamical horizon frameworks.Comment: 39 pages, 3 figures, Final Version : content essentially unchanged but many small improvements made in response to referees, a few references adde

Prospects for joint radio telescope and gravitational wave searches for astrophysical transients

The radio skies remain mostly unobserved when it comes to transient phenomena. The direct detection of gravitational waves will mark a major milestone of modern astronomy, as an entirely new window will open on the universe. Two apparently independent phenomena can be brought together in a coincident effort that has the potential to boost both searches. In this paper we will outline the scientific case that stands behind these future joint observations and will describe the methods that might be used to conduct the searches and analyze the data. The targeted sources are binary systems of compact objects, known to be strong candidate sources for gravitational waves. Detection of transients coincident in these two channels would be a significant smoking gun for first direct detection of gravitational waves, and would open up a new field for characterization of astrophysical transients involving massive compact objects.Comment: 12 pages, Amaldi 8 Conference (New York, 2009) proceedings pape

A List of Galaxies for Gravitational Wave Searches

We present a list of galaxies within 100 Mpc, which we call the Gravitational Wave Galaxy Catalogue (GWGC), that is currently being used in follow-up searches of electromagnetic counterparts from gravitational wave searches. Due to the time constraints of rapid follow-up, a locally available catalogue of reduced, homogenized data is required. To achieve this we used four existing catalogues: an updated version of the Tully Nearby Galaxy Catalog, the Catalog of Neighboring Galaxies, the V8k catalogue and HyperLEDA. The GWGC contains information on sky position, distance, blue magnitude, major and minor diameters, position angle, and galaxy type for 53,255 galaxies. Errors on these quantities are either taken directly from the literature or estimated based on our understanding of the uncertainties associated with the measurement method. By using the PGC numbering system developed for HyperLEDA, the catalogue has a reduced level of degeneracies compared to catalogues with a similar purpose and is easily updated. We also include 150 Milky Way globular clusters. Finally, we compare the GWGC to previously used catalogues, and find the GWGC to be more complete within 100 Mpc due to our use of more up-to-date input catalogues and the fact that we have not made a blue luminosity cut.Comment: Accepted for publication in Classical and Quantum Gravity, 13 pages, 7 figure

Supersymmetric isolated horizons

We construct a covariant phase space for rotating weakly isolated horizons in Einstein-Maxwell-Chern-Simons theory in all (odd) $D\geq5$ dimensions. In particular, we show that horizons on the corresponding phase space satisfy the zeroth and first laws of black-hole mechanics. We show that the existence of a Killing spinor on an isolated horizon in four dimensions (when the Chern-Simons term is dropped) and in five dimensions requires that the induced (normal) connection on the horizon has to vanish, and this in turn implies that the surface gravity and rotation one-form are zero. This means that the gravitational component of the horizon angular momentum is zero, while the electromagnetic component (which is attributed to the bulk radiation field) is unconstrained. It follows that an isolated horizon is supersymmetric only if it is extremal and nonrotating. A remarkable property of these horizons is that the Killing spinor only has to exist on the horizon itself. It does not have to exist off the horizon. In addition, we find that the limit when the surface gravity of the horizon goes to zero provides a topological constraint. Specifically, the integral of the scalar curvature of the cross sections of the horizon has to be positive when the dominant energy condition is satisfied and the cosmological constant $\Lambda$ is zero or positive, and in particular rules out the torus topology for supersymmetric isolated horizons (unless $\Lambda<0$) if and only if the stress-energy tensor $T_{ab}$ is of the form such that $T_{ab}\ell^{a}n^{b}=0$ for any two null vectors $\ell$ and $n$ with normalization $\ell_{a}n^{a}=-1$ on the horizon.Comment: 26 pages, 1 figure; v2: typos corrected, topology arguments corrected, discussion of black rings and dipole charge added, references added, version to appear in Classical and Quantum Gravit

Edge-control and surface-smoothness in sub-aperture polishing of mirror segments

This paper addresses two challenges in establishing a new process chain for polishing hexagonal segments for extremely large telescopes:- i) control of edge and corner profiles in small-tool polishing of hexagons, and ii) achieving the required smoothness of the bulk aspheric form. We briefly describe the performance of a CNC-grinding process used to create the off-axis asphere, which established the input-quality for subsequent processing. We then summarize processes for smoothing ground mid-spatials and pre- and corrective polishing using Zeeko CNC machines. The impact of two cases is considered; i) all processing stages are performed after the segment is cut hexagonal, and ii) final rectification of a hexagon after cutting from an aspherised roundel, as an alternative to ionfiguring. We then report on experimental results on witness samples demonstrating edges and corners close to the EELT segment specification, and results on a full-aperture spherical segment showing excellent surface smoothness. © 2012 SPIE

Predicting phase equilibria in polydisperse systems

Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed Matter; uses Institute of Physics style file iopart.cls (included