The Microcanonical Functional Integral. I. The Gravitational Field

The gravitational field in a spatially finite region is described as a microcanonical system. The density of states $\nu$ is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by {\it any} real stationary axisymmetric black hole, then in this same approximation $\ln\nu$ is shown to equal 1/4 the area of the black hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of $\nu$ that lead to "imaginary time" functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.Comment: 29 pages, plain Te

Trumpet slices of the Schwarzschild-Tangherlini spacetime

We study families of time-independent maximal and 1+log foliations of the Schwarzschild-Tangherlini spacetime, the spherically-symmetric vacuum black hole solution in D spacetime dimensions, for D >= 4. We identify special members of these families for which the spatial slices display a trumpet geometry. Using a generalization of the 1+log slicing condition that is parametrized by a constant n we recover the results of Nakao, Abe, Yoshino and Shibata in the limit of maximal slicing. We also construct a numerical code that evolves the BSSN equations for D=5 in spherical symmetry using moving-puncture coordinates, and demonstrate that these simulations settle down to the trumpet solutions.Comment: 11 pages, 6 figures, submitted to PR

Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation

Quantum stress-energy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $\Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {\it all} regular renormalized stress-energy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $\Delta S$ has a local minimum there. Explicit calculation shows that indeed $\Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stress-energy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the back-reaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $\Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The back-reaction, no matter how "small",Comment: 19 pages, RevTe

Action Principle for the Generalized Harmonic Formulation of General Relativity

An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona--Casas and Palenzuela (BBP). The relationship between the generalized harmonic action and the BBP action is discussed in detail.Comment: This version is contains more thorough presentations and discussions of the key results. To be published in PRD. (8 pages, no figures

Modifying the Einstein Equations off the Constraint Hypersuface

A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.Comment: 4 pages, 1 figure, uses REVTe

Experimental Observation Of Energetic Ions Accelerated By Three-Dimensional Magnetic Reconnection In A Laboratory Plasma

Magnetic reconnection is widely believed responsible for heating the solar corona as well as for generating X-rays and energetic particles in solar flares. On astrophysical scales, reconnection in the intergalactic plasma is a prime candidate for a local source (Mpc) of cosmic rays exceeding the Greisen-Zatsepin-Kuzmin cutoff (∼10(19) eV). In a laboratory astrophysics experiment, we have made the first observation of particles accelerated by magnetic reconnection events to energies significantly above both the thermal and the characteristic magnetohydrodynamic energies. These particles are correlated temporally and spatially with the formation of three-dimensional magnetic structures in the reconnection region

rotl: an R package to interact with the Open Tree of Life data

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135519/1/mee312593_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135519/2/mee312593.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135519/3/mee312593-sup-0001-AppendixS1.pd

Evolution of the UV Excess in Early-Type Galaxies

We examine the UV emission from luminous early-type galaxies as a function of redshift. We perform a stacking analysis using Galaxy Evolution Explorer (GALEX) images of galaxies in the NOAO Deep Wide Field Survey (NDWFS) Bo\"otes field and examine the evolution in the UV colors of the average galaxy. Our sample, selected to have minimal ongoing star formation based on the optical to mid-IR SEDs of the galaxies, includes 1843 galaxies spanning the redshift range $0.05\leq z\leq0.65$. We find evidence that the strength of the UV excess decreases, on average, with redshift, and our measurements also show moderate disagreement with previous models of the UV excess. Our results show little evolution in the shape of the UV continuum with redshift, consistent either with the binary model for the formation of Extreme Horizontal Branch (EHB) stars or with no evolution in EHB morphology with look-back time. However, the binary formation model predicts that the strength of the UV excess should also be relatively constant, in contradiction with our measured results. Finally, we see no significant influence of a galaxy's environment on the strength of its UV excess.Comment: 30 pages, 10 figures; accepted by ApJ. Modified from original version to reflect referee's comment

Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy

We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system $\Sigma$ contained within a finite topologically spherical boundary $B = \partial \Sigma$. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values.Comment: REVTEX, 16 pages, 1 figur