Gravitational energy

Observers at rest in a stationary spacetime flat at infinity can measure small amounts of rest-mass+internal energies+kinetic energies+pressure energy in a small volume of fluid attached to a local inertial frame. The sum of these small amounts is the total "matter energy" for those observers. The total mass-energy minus the matter energy is the binding gravitational energy. Misner, Thorne and Wheeler evaluated the gravitational energy of a spherically symmetric static spacetime. Here we show how to calculate gravitational energy in any static and stationary spacetime for isolated sources with a set of observers at rest. The result of MTW is recovered and we find that electromagnetic and gravitational 3-covariant energy densities in conformastatic spacetimes are of opposite signs. Various examples suggest that gravitational energy is negative in spacetimes with special symmetries or when the energy-momentum tensor satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra

Integral Constraints On cosmological Perturbations and their Energy

We show the relation between Traschen's integral equations and the energy, and ``position of the centre of mass'', of the matter perturbations in a Robertson-Walker spacetime. When the perturbations are ``localised'' we get a set of integral constraints that includes hers. We illustrate them on a simple example.Comment: 19 pages, Tex file, submitted to Classical and Quantum Gravit

Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator

We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the results are very promising. We also present a detailed computation of the spectrum and chiral properties of the Schwinger Model in the overlap lattice formulation.Comment: Lattice 2000 (Chiral Fermions

The growth of galaxies in cosmological simulations of structure formation

We use hydrodynamic simulations to examine how the baryonic components of galaxies are assembled, focusing on the relative importance of mergers and smooth accretion in the formation of ~L_* systems. In our primary simulation, which models a (50\hmpc)^3 comoving volume of a Lambda-dominated cold dark matter universe, the space density of objects at our (64-particle) baryon mass resolution threshold, M_c=5.4e10 M_sun, corresponds to that of observed galaxies with L~L_*/4. Galaxies above this threshold gain most of their mass by accretion rather than by mergers. At the redshift of peak mass growth, z~2, accretion dominates over merging by about 4:1. The mean accretion rate per galaxy declines from ~40 M_sun/yr at z=2 to ~10 M_sun/yr at z=0, while the merging rate peaks later (z~1) and declines more slowly, so by z=0 the ratio is about 2:1. We cannot distinguish truly smooth accretion from merging with objects below our mass resolution threshold, but extrapolating our measured mass spectrum of merging objects, dP/dM ~ M^a with a ~ -1, implies that sub-resolution mergers would add relatively little mass. The global star formation history in these simulations tracks the mass accretion rate rather than the merger rate. At low redshift, destruction of galaxies by mergers is approximately balanced by the growth of new systems, so the comoving space density of resolved galaxies stays nearly constant despite significant mass evolution at the galaxy-by-galaxy level. The predicted merger rate at z<~1 agrees with recent estimates from close pairs in the CFRS and CNOC2 redshift surveys.Comment: Submitted to ApJ, 35 pp including 15 fig

The dark side of humanity scale: A reconstruction of the Dark Tetrad constructs

There has been an absence of consideration regarding measurement invariance across males and females in the widely available Dark Tetrad (DT) scales which measure psychopathy, Machiavellianism, narcissism and everyday sadism. This has resulted in criticisms of the measures, suggesting that the assessed constructs are not wholly relatable between the groups. This article documents the construction and validation of the Dark Side of Humanity Scale (DSHS), which measures dark personalities from an alternative viewpoint, determined by the constructs as they emerged from the male and female data, whilst aligning with theory and attaining invariance between sex. Across four samples (n = 2409), using a diverse range of statistical methods, including exploratory graph analysis, item response theory and confirmatory factor analysis, a divergence from the widely available DT measures emerged, whereby primary psychopathy and Machiavellianism were unified. This corroborated past research which had discussed the two constructs as being parallel. It further supported the DSHS with a shift away from the traditional DT conceptualisation. The resulting scale encompasses four factors which are sex invariant across samples and time. The first factor represents the successful psychopath, factor two addresses the grandiose form of entitlement, factor three taps into everyday sadism whilst the fourth factor pertains to narcissistic entitlement rage. Construct and external validity of the DSHS across two samples (n = 1338), as well as test-retest reliability (n = 413), was achieved. The DSHS provides an alternative approach to investigating the dark side of human nature, whilst also being sex invariant, thus making it highly suitable for use with mixed sex samples

The catalog of radial velocity standard stars for the Gaia RVS: status and progress of the observations

A new full-sky catalog of Radial Velocity standard stars is being built for the determination of the Radial Velocity Zero Point of the RVS on board of Gaia. After a careful selection of 1420 candidates matching well defined criteria, we are now observing all of them to verify that they are stable enough over several years to be qualified as reference stars. We present the status of this long-term observing programme on three spectrographs : SOPHIE, NARVAL and CORALIE, complemented by the ELODIE and HARPS archives. Because each instrument has its own zero-point, we observe intensively IAU RV standards and asteroids to homogenize the radial velocity measurements. We can already estimate that ~8% of the candidates have to be rejected because of variations larger than the requested level of 300 m/s.Comment: Proceedings of SF2A2010, S. Boissier, M. Heydari-Malayeri, R. Samadi and D. Valls-Gabaud (eds), 3 pages, 2 figure