Integrability of the Minimal Strain Equations for the Lapse and Shift in 3+1 Numerical Relativity

Brady, Creighton and Thorne have argued that, in numerical relativity simulations of the inspiral of binary black holes, if one uses lapse and shift functions satisfying the ``minimal strain equations'' (MSE), then the coordinates might be kept co-rotating, the metric components would then evolve on the very slow inspiral timescale, and the computational demands would thus be far smaller than for more conventional slicing choices. In this paper, we derive simple, testable criteria for the MSE to be strongly elliptic, thereby guaranteeing the existence and uniqueness of the solution to the Dirichlet boundary value problem. We show that these criteria are satisfied in a test-bed metric for inspiraling binaries, and we argue that they should be satisfied quite generally for inspiraling binaries. If the local existence and uniqueness that we have proved holds globally, then, for appropriate boundary values, the solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and keeps the metric evolving slowly) will be the unique solution and thus should be reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the uniqueness of the solution to the Dirichlet problem clarified. New subsection on the nature of the boundary dat

Evolution of Binary Black Hole Spacetimes

We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.Comment: 4 pages, 3 figure

Final spin of a coalescing black-hole binary: an Effective-One-Body approach

We update the analytical estimate of the final spin of a coalescing black-hole binary derived within the Effective-One-Body (EOB) approach. We consider unequal-mass non-spinning black-hole binaries. It is found that a more complete account of relevant physical effects (higher post-Newtonian accuracy, ringdown losses) allows the {\it analytical} EOB estimate to `converge towards' the recently obtained {\it numerical} results within 2%. This agreement illustrates the ability of the EOB approach to capture the essential physics of coalescing black-hole binaries. Our analytical approach allows one to estimate the final spin of the black hole formed by coalescing binaries in a mass range ($\nu=m_1m_2/(m_1+m_2)^2 < 0.16$) which is not presently covered by numerical simulations.Comment: 8 pages, two figures. To appear in Phys. Rev.

Perturbative Charged Rotating 5D Einstein-Maxwell Black Holes

We present perturbative charged rotating 5D Einstein-Maxwell black holes with spherical horizon topology. The electric charge Q is the perturbative parameter, the perturbations being performed up to 4th order. The expressions for the relevant physical properties of these black holes are given. The gyromagnetic ratio g, in particular, is explicitly shown to be non-constant in higher order, and thus to deviate from its lowest order value, g=3. Comparison of the perturbative analytical solutions with their non-perturbative numerical counterparts shows remarkable agreement.Comment: RevTeX style, 4 pages, 5 figure

3.4 Million Real-World Learning Management System Logins Reveal the Majority of Students Experience Social Jet Lag Correlated with Decreased Performance

Misalignments between endogenous circadian rhythms and the built environment (i.e., social jet lag, SJL) result in learning and attention deficits. Currently, there is no way to assess the impact of SJL on learning outcomes of large populations as a response to schedule choices, let alone to assess which individuals are most negatively impacted by these choices. We analyzed two years of learning management system login events for 14,894 Northeastern Illinois University (NEIU) students to investigate the capacity of such systems as tools for mapping the impact of SJL over large populations while maintaining the ability to generate insights about individuals. Personal daily activity profiles were validated against known biological timing effects, and revealed a majority of students experience more than 30 minutes of SJL on average, with greater amplitude correlating strongly with a significant decrease in academic performance, especially in people with later apparent chronotypes. Our findings demonstrate that online records can be used to map individual- and population-level SJL, allow deep mining for patterns across demographics, and could guide schedule choices in an effort to minimize SJL’s negative impact on learning outcomes

The Collision of Two Black Holes

We study the head-on collision of two equal mass, nonrotating black holes. We consider a range of cases from holes surrounded by a common horizon to holes initially separated by about $20M$, where $M$ is the mass of each hole. We determine the waveforms and energies radiated for both the $\ell = 2$ and $\ell=4$ waves resulting from the collision. In all cases studied the normal modes of the final black hole dominate the spectrum. We also estimate analytically the total gravitational radiation emitted, taking into account the tidal heating of horizons using the membrane paradigm, and other effects. For the first time we are able to compare analytic calculations, black hole perturbation theory, and strong field, nonlinear numerical calculations for this problem, and we find excellent agreement.Comment: 14 pages, 93-

Head-on infall of two compact objects: Third post-Newtonian Energy Flux

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.Comment: 25 pages, 2 figures, This version includes the changes appearing in the Erratum published in Phys. Rev.

Sex differences in variability across timescales in BALB/c mice.

BackgroundFemales are markedly underinvestigated in the biological and behavioral sciences due to the presumption that cyclic hormonal changes across the ovulatory cycle introduce excess variability to measures of interest in comparison to males. However, recent analyses indicate that male and female mice and rats exhibit comparable variability across numerous physiological and behavioral measures, even when the stage of the estrous cycle is not considered. Hormonal changes across the ovulatory cycle likely contribute cyclic, intra-individual variability in females, but the source(s) of male variability has, to our knowledge, not been investigated. It is unclear whether male variability, like that of females, is temporally structured and, therefore, quantifiable and predictable. Finally, whether males and females exhibit variability on similar time scales has not been explored.MethodsThese questions were addressed by collecting chronic, high temporal resolution locomotor activity (LA) and core body temperature (CBT) data from male and female BALB/c mice.ResultsContrary to expectation, males are more variable than females over the course of the day (diel variability) and exhibit higher intra-individual daily range than females in both LA and CBT. Between mice of a given sex, variability is comparable for LA but the inter-individual daily range in CBT is greater for males. To identify potential rhythmic processes contributing to these sex differences, we employed wavelet transformations across a range of periodicities (1-39&nbsp;h).ConclusionsAlthough variability in circadian power is comparable between the sexes for both LA and CBT, infradian variability is greater in females and ultradian variability is greater in males. Thus, exclusion of female mice from studies because of estrous cycle variability may increase variance in investigations where only male measures are collected over a span of several hours and limit generalization of findings from males to females

Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems

Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two non-spinning compact objects moving on circular orbits with frequency Omega, at leading order beyond the test-particle approximation. By minimizing E(Omega) we recover the exact frequency shift of the Schwarzschild innermost stable circular orbit induced by the conservative piece of the gravitational self-force. Comparing our results for the coordinate invariant relation E(J) to those recently obtained from numerical simulations of comparable-mass non-spinning black-hole binaries, we find a remarkably good agreement, even in the strong-field regime. Our findings confirm that the domain of validity of perturbative calculations may extend well beyond the extreme mass-ratio limit.Comment: 5 pages, 1 figure; matches the published versio

The Rest-Frame Instant Form of Relativistic Perfect Fluids and of Non-Dissipative Elastic Materials

For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an action principle depending only on their Lagrange coordinates $\alpha^i(x)$ without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to non-dissipative relativistic elastic materials described in terms of Lagrangian coordinates.Comment: revtex file, 70 page