Two physical characteristics of numerical apparent horizons

This article translates some recent results on quasilocal horizons into the language of $(3+1)$ general relativity so as to make them more useful to numerical relativists. In particular quantities are described which characterize how quickly an apparent horizon is evolving and how close it is to either equilibrium or extremality.Comment: 6 pages, 2 figures, conference proceedings loosely based on talk given at Theory Canada III (Edmonton, Alberta, 2007). V2: Minor changes in response to referees comments to improve clarity and fix typos. One reference adde

Tax Policy and Returns to Education

This paper considers how asymmetric tax treatment, where labour market earnings are taxed but household production is untaxed, aspects educational choice and labour supply. We show that taxes on labour market earnings can generate a large (non-marginal) switch to home production and the ensuing deadweight losses are large. Using a cross-country panel, we find that gender differences in labour supply responses to tax policy can explain differences in aggregate labour supply and years of education across countries.Increasing returns; tax policy; gender; labour supply; education

Extremality conditions for isolated and dynamical horizons

A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a parameter e which characterizes how close a horizon is to extremality and should be calculable in numerical simulations.Comment: 13 pages, 4 figures, added reference; v3 appendix added with proof of result from section IIID, some discussion and references added. Version to appear in PR

Stationary untrapped boundary conditions in general relativity

A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities for the quasi-local regions. If on the boundary the evolution vector normal to the 2-surface is chosen to be proportional to the dual expansion vector, we obtain a generalization of the Hawking energy associated with a generalized Kodama vector. This vector plays the role for the stationary untrapped boundary conditions which the stationary Killing vector plays for stationary black holes. When the dual expansion vector is null, the boundary conditions reduce to the ones given by the non-expanding horizons and the null trapping horizons.Comment: 11 pages, improved discussion section, a reference added, accepted for publication in Classical and Quantum Gravit

Comparative Monte Carlo Efficiency by Monte Carlo Analysis

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the $\lambda_2$ of various Markov chain transition matrices. We first computed ${\lambda_2}$ for several one and two dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as a function of temperature and applied magnetic field. Next, we computed $\lambda_2$ for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size $\Delta$. Based on the $\lambda_2$ criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule-of-thumb of adjusting $\Delta$ so the Metropolis acceptance rate is around 50% range is often sub-optimal. In general, as a function of temperature or $\Delta$, $\lambda_2$ for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure

Fundamental properties and applications of quasi-local black hole horizons

The traditional description of black holes in terms of event horizons is inadequate for many physical applications, especially when studying black holes in non-stationary spacetimes. In these cases, it is often more useful to use the quasi-local notions of trapped and marginally trapped surfaces, which lead naturally to the framework of trapping, isolated, and dynamical horizons. This framework allows us to analyze diverse facets of black holes in a unified manner and to significantly generalize several results in black hole physics. It also leads to a number of applications in mathematical general relativity, numerical relativity, astrophysics, and quantum gravity. In this review, I will discuss the basic ideas and recent developments in this framework, and summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th International Conference on General Relativity and Gravitation, 8-13 July 2007, Sydney, Australi

Molecular clouds in the centers of galaxies: Constraints from HCN and CO-13 line emission

We have searched for HCN J=1-0 line emission in the centers of 12 galaxies and have detected it in 10 of them. We have obtained complementary data on J=1-0 and 2-1 transitions of CO-12 and CO-13 in these systems. The ratio of integrated intensities, I(CO 1-0)/I(HCN 1-0) = 25 +/- 11 for this sample. We find that HCN emission of this strength can be produced under conditions of subthermal excitation. In combination with the line ratios in CO and CO-13, HCN puts constraints on the mean conditions of molecular clouds and on the mix of cloud types within the projected beam

Worker heterogeneity, new monopsony, and training

A worker's output depends not only on his/her own ability but also on that of colleagues, who can facilitate the performance of tasks that each individual cannot accomplish on his/her own. We show that this common-sense observation generates monopsony power and is sufficient to explain why employers might expend resources on training employees even when the training is of use to other firms. We show that training will take place in better-than-average or ‘good’ firms enjoying greater monopsony power, whereas ‘bad’ firms will have low-ability workers unlikely to receive much training

Process for extracting ethanol from fermentation broths for direct blending into gasoline while preserving the broth for recycling

Describes a method of producing ethanol from a fermentation source for direct blending into gasoline to form gasohol by extracting ethanol from the fermentation broth with a non-toxic solvent compatible with gasoline. The invention includes extraction outside of the fermentor and the recycling of the extracted broth back to the fermentor. An extracting column is used for the extraction and recycling and the extract can be dried before blending it with the gasoline. The preferred solvent is an alkylate