Simulating extreme-mass-ratio systems in full general relativity

We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract off its contribution to the truncation error, thereby more efficiently achieving a desired level of accuracy. We demonstrate the method by applying it to the radial infall of a solar-type star into supermassive black holes with mass ratios $\geq 10^6$. The self-gravity of the star is thus consistently modeled within the context of general relativity, and the star's interaction with the black hole computed with moderate computational cost, despite the over five orders of magnitude difference in gravitational potential (as defined by the ratio of mass to radius). We compute the tidal deformation of the star during infall, and the gravitational wave emission, finding the latter is close to the prediction of the point-particle limit.Comment: 6 pages, 5 figures; added one figure, revised to match PRD RC versio

Ultrarelativistic black hole formation

We study the ultrarelativistic head-on collision of equal mass particles, modeled as self-gravitating fluid spheres, by numerically solving the coupled Einstein-hydrodynamic equations. We focus on cases well within the kinetic energy dominated regime, where between 88-92% ($\gamma=8$ to 12) of the initial net energy of the spacetime resides in the translation kinetic energy of the particles. We find that for sufficiently large boosts, black hole formation occurs. Moreover, near yet above the threshold of black hole formation, the collision initially leads to the formation of two distinct apparent horizons that subsequently merge. We argue that this can be understood in terms of a focusing effect, where one boosted particle acts as a gravitational lens on the other and vice versa, and that this is further responsible for the threshold being lower (by a factor of a few) compared to simple hoop conjecture estimates. Cases slightly below threshold result in complete disruption of the model particles. The gravitational radiation emitted when black holes form reaches luminosities of 0.014 $c^5/G$, carrying $16\pm2$ of the total energy.Comment: 5 pages, 4 figures; revised to match PRL versio

Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes

We study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca equations. We concentrate on a rapidly spinning black hole ($a=0.99$) and the dominant $m=1$ azimuthal mode of the Proca field, with real and imaginary components of the field chosen to yield an axisymmetric stress-energy tensor and, hence, spacetime. We find that in excess of $9\%$ of the black hole's mass can be transferred into the field. In all cases studied, the superradiant instability smoothly saturates when the black hole's horizon frequency decreases to match the frequency of the Proca cloud that spontaneously forms around the black hole.Comment: 6 pages, 6 figures; revised to match PRL versio

Lorentz-noninvariant neutrino oscillations: model and predictions

We present a three-parameter neutrino-oscillation model for three flavors of massless neutrinos with Fermi-point splitting and tri-maximal mixing angles. One of these parameters is the T-violating phase \epsilon, for which the experimental results from K2K and KamLAND appear to favor a nonzero value. In this article, we give further model predictions for neutrino oscillations. Upcoming experiments will be able to test this simple model and the general idea of Fermi-point splitting. Possible implications for proposed experiments and neutrino factories are also discussed.Comment: 22 pages, v5: final version to appear in IJMP

Eccentric mergers of black holes with spinning neutron stars

We study dynamical capture binary black hole-neutron star (BH-NS) mergers focusing on the effects of the neutron star spin. These events may arise in dense stellar regions, such as globular clusters, where the majority of neutron stars are expected to be rapidly rotating. We initialize the BH-NS systems with positions and velocities corresponding to marginally unbound Newtonian orbits, and evolve them using general-relativistic hydrodynamical simulations. We find that even moderate spins can significantly increase the amount of mass in unbound material. In some of the more extreme cases, there can be up to a third of a solar mass in unbound matter. Similarly, large amounts of tidally stripped material can remain bound and eventually accrete onto the BH---as much as a tenth of a solar mass in some cases. These simulations demonstrate that it is important to treat neutron star spin in order to make reliable predictions of the gravitational wave and electromagnetic transient signals accompanying these sources.Comment: 7 pages, 4 figures; revised to match published versio

Black Hole Superradiance in Dynamical Spacetime

We study the superradiant scattering of gravitational waves by a nearly extremal black hole (dimensionless spin $a=0.99$) by numerically solving the full Einstein field equations, thus including backreaction effects. This allows us to study the dynamics of the black hole as it loses energy and angular momentum during the scattering process. To explore the nonlinear phase of the interaction, we consider gravitational wave packets with initial energies up to $10$ of the mass of the black hole. We find that as the incident wave energy increases, the amplification of the scattered waves, as well as the energy extraction efficiency from the black hole, is reduced. During the interaction the apparent horizon geometry undergoes sizable nonaxisymmetric oscillations. The largest amplitude excitations occur when the peak frequency of the incident wave packet is above where superradiance occurs, but close to the dominant quasinormal mode frequency of the black hole.Comment: 5 pages, 4 figures; revised to match PRD versio

Observing complete gravitational wave signals from dynamical capture binaries

We assess the detectability of the gravitational wave signals from highly eccentric compact binaries. We use a simple model for the inspiral, merger, and ringdown of these systems. The model is based on mapping the binary to an effective single black hole system described by a Kerr metric, thereby including certain relativistic effects such as zoom-whirl-type behavior. The resultant geodesics source quadrupolar radiation and, in turn, are evolved under its dissipative effects. At the light ring, we attach a merger model that was previously developed for quasicircular mergers but also performs well for eccentric mergers with little modification. We apply this model to determine the detectability of these sources for initial, Enhanced, and Advanced LIGO across the parameter space of nonspinning close capture compact binaries. We conclude that, should these systems exist in nature, the vast majority will be missed by conventional burst searches or by quasicircular waveform templates in the advanced detector era. Other methods, such as eccentric templates or, more practically, a stacked excess power search, must be developed to avoid losing these sources. These systems would also have been missed frequently in the initial LIGO data analysis. Thus, previous null coincidence results with detected gamma-ray bursts cannot exclude the possibility of coincident gravitational wave signals from eccentric binaries.Comment: 18 pages, 18 figures; revised to match accepted version, PRD in pres

Time dilation in dynamic visual display

How does the brain estimate time? This old question has led to many biological and psychological models of time perception (R. A. Block, 1989; P. Fraisse, 1963; J. Gibbon, 1977; D. L. I. Zakay, 1989). Because time cannot be directly measured at a given moment, it has been proposed that the brain estimates time based on the number of changes in an event (S. W. Brown, 1995; P. Fraisse, 1963; W. D. Poynter, 1989). Consistent with this idea, dynamic visual stimuli are known to lengthen perceived time (J. F. Brown, 1931; S. Goldstone & W. T. Lhamon, 1974; W. T. Lhamon & S. Goldstone, 1974, C. O. Z. Roelofs & W. P. C. Zeeman, 1951). However, the kind of information that constitutes the basis for time perception remains unresolved. Here, we show that the temporal frequency of a stimulus serves as the “clock” for perceived duration. Other aspects of changes, such as speed or coherence, were found to be inconsequential. Time dilation saturated at a temporal frequency of 4–8 Hz. These results suggest that the clock governing perceived time has its basis at early processing stages. The possible links between models of time perception and neurophysiological functions of early visual areas are discussed

The Swiss and Dutch Health Insurance Systems: Universal Coverage and Regulated Competitive Insurance Markets

Compares systems of universal insurance coverage based on individual mandates, consumer choice of health plans, and regulated insurance market competition in Switzerland and the Netherlands. Discusses insights and implications for U.S. reform efforts