119440102
Conformal invariance and the conformal-traceless decomposition of the gravitational field
Einstein’s theory of general relativity is written in terms of the variables obtained from a conformaltraceless decomposition of the spatial metric and extrinsic curvature. The determinant of the conformal metric is not restricted, so the action functional and equations of motion are invariant under conformal transformations. With this approach the conformal-traceless variables remain free of density weights. The conformal invariance of the equations of motion can be broken by imposing an evolution equation for the determinant of the conformal metric g. Two conditions are considered, one in which g is constant in time and one in which g is constant along the unit normal to the spacelike hypersurfaces. This approach is used to write the Baumgarte-Shapiro-Shibata-Nakamura system of evolution equations in conformally invariant form. The presentation includes a discussion of the conformal thin sandwich construction of gravitational initial data, and the conformal flatness condition as an approximation to the evolution equations.
119986427
On the Poisson brackets of differentiable generators in classical field theory
The canonical formulation of field theory on open spaces is considered. It is proved, under appropriate assumptions, that the Poisson bracket of two differentiable generators is also a differentiable generator.
16734842
Black Hole Thermodynamics in a Box
Simple calculations indicate that the partition function for a black hole is defined only if the temperature is fixed on a finite boundary. Consequences of this result are discussed. (Contribution to the Proceedings of the Lanczos Centenary Conference.)
119005465
Modifying the Einstein equations off the constraint hypersurface
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.
6269112
Action functionals for relativistic perfect fluids
Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.
16432578
Dust as a standard of space and time in canonical quantum gravity.
The coupling of the metric to an incoherent dust introduces into spacetime a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become canonical coordinates in the phase space of the system. The Hamiltonian constraint can be resolved with respect to the momentum that is canonically conjugate to the dust time. Formal imposition of the resolved constraint as an operator restriction on the quantum states yields a functional Schr\"odinger equation. The ensuing Hamiltonian density has an extraordinary feature: it depends only on the geometric variables, not on the dust coordinates or time. This has three important consequences. First, the functional Schr\"odinger equation can be solved by separating the dust time from the geometric variables. Second, disregarding the standard factor-ordering difficulties, the Hamiltonian densities strongly commute and therefore can be simultaneously defined by spectral analysis. Third, the standard constraint system of vacuum gravity is cast into a form in which it generates a true Lie algebra. The particles of dust introduce into space a privileged system of coordinates that allows the supermomentum constraint to be solved explicitly. The Schr\"odinger equation yields a formally conserved inner product that can be written in terms of either the instantaneous state functionals or the solutions of constraints. Gravitational observables admit a similar dual representation. Examples of observables are given, though neither the intrinsic metric nor the extrinsic curvature are observables. This comes as close as one can reasonably expect to a satisfactory phenomenological quantization scheme that is free of most of the problems of time.
51807515
Data formats for numerical relativity waves
This document proposes data formats to exchange numerical relativity results, in particular gravitational waveforms. The primary goal is to further the interaction between gravitational-wave source modeling groups and the gravitational-wave data-analysis community. We present a simple and extendable format which is applicable to various kinds of gravitational wave sources including binaries of compact objects and systems undergoing gravitational collapse, but is nevertheless sufficiently general to be useful for other purposes.
16002528
Testing the LIGO inspiral analysis with hardware injections
Injection of simulated binary inspiral signals into detector hardware provides an excellent test of the inspiral detection pipeline. By recovering the physical parameters of an injected signal, we test our understanding of both instrumental calibration and the data analysis pipeline. We describe an inspiral search code and results from hardware injection tests and demonstrate that injected signals can be recovered by the data analysis pipeline. The parameters of the recovered signals match those of the injected signals.
123343445
Status of the g-2 experiment at BNL
The muon g-2 experiment at Brookhaven has successfully completed two exploratory runs using pion injection and direct muon injection for checkout and initial data taking. The main components of the experiment, which include the pion beam line, the superconducting storage ring and inflector magnets, the muon kicker and the lead-scintillating fiber calorimeters have been satisfactorily commissioned. First results on the anomalous magnetic moment of the positive muon from pion injection are in good agreement with previous experimental results for a(mu+) and a(mu-) from CERN and of comparable accuracy (13 ppm). Analysis of the 1998 muon injection run is in progress and expected to improve the precision to about 4 ppm. A first production run is scheduled for January 1999 with the goal of reaching the 1 ppm error level.
41266047
Model waveform accuracy standards for gravitational wave data analysis
Model waveforms are used in gravitational wave data analysis to detect and then to measure the properties of a source by matching the model waveforms to the signal from a detector. This paper derives accuracy standards for model waveforms which are sufficient to ensure that these data analysis applications are capable of extracting the full scientific content of the data, but without demanding excessive accuracy that would place undue burdens on the model waveform simulation community. These accuracy standards are intended primarily for broadband model waveforms produced by numerical simulations, but the standards are quite general and apply equally to such waveforms produced by analytical or hybrid analytical-numerical methods.
125126984
The CDF forward electromagnetic calorimeter