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

Improving the potential of pixel-based supervised classification in the absence of quality ground truth data

The accuracy of classified results is often measured in comparison with reference or “ground truth” information. However, in inaccessible or remote natural areas, sufficient ground truth data may not be cost-effectively acquirable. In such cases investigative measures towards the optimisation of the classification process may be required. The goal of this paper was to describe the impact of various parameters when applying a supervised Maximum Likelihood Classifier (MLC) to SPOT 5 image analysis in a remote savanna biome. Pair separation indicators and probability thresholds were used to analyse the effect of training area size and heterogeneity as well as band combinations and the use of vegetation indices. It was found that adding probability thresholds to the classification may provide a measure of suitability regarding training area characteristics and band combinations. The analysis illustrated that finding a balance between training area size and heterogeneity may be fundamental to achieving an optimum classified result.Furthermore, results indicated that the addition of vegetation index values introduced as additional image bands could potentially improve classified products and that threshold outcomes could be used to illustrate confidence levels when mapping classified results

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

Banishment: Germiston's answer to opposition in Natalspruit Location, 1955-1957

Paper presented at the Wits History Workshop: The Making of Class, 9-14 February, 198

The development of a spatial decision support system to optimise agricultural resource use in the Western Cape

This paper describes the development of a decision support model for regional agricultural resource utilisation. The analysis was generated in a spatial context and the optimisation technique was interactive with a geographical information system (GIS). Economic and operational research methodologies were linked to the GIS in the process of determining the appropriate resource uses for the region. The optimisation technique was applied for the Western Cape Province for eight crops. The results of this research are discussed in this paper, with specific reference to its application value for the public sector and agri-business.Farm Management, Resource /Energy Economics and Policy,

Meningiomas occurring during long-term survival after treatment for childhood cancer

Childhood cancer is rare but improvements in treatment over the past five decades have resulted in a cohort of more than 30,000 long-term survivors of childhood cancer in the UK with more added annually. These long-term survivors are at risk of late effects of cancer treatment which replace original tumour recurrence as the leading cause of premature death. Second neoplasms are a particular risk and in the central nervous system meningiomas occur increasingly with increased radiation dose to central nervous system tissue and length of time after exposure, resulting in a 500-fold increase above that expected in the normal population by 40 years of follow up. This multidisciplinary author group and others met to discuss the issue. Our pooled information, and consensus that screening should only follow symptoms, was published online by the Royal College of Radiologists in 2013. We outline here the current knowledge and management of these neoplasms secondary to childhood cancer treatment