119127453
Puncture Evolution of Schwarzschild Black Holes
The moving puncture method is analyzed for a single, nonspinning black hole. It is shown that the puncture region is not resolved by current numerical codes. As a result, the geometry near the puncture appears to evolve to an infinitely long cylinder of finite areal radius. The puncture itself actually remains at spacelike infinity throughout the evolution. In the limit of infinite resolution the data never become stationary. However, at any reasonable finite resolution the grid points closest to the puncture are rapidly drawn into the black hole interior by the {gamma}-driver shift condition. The data can then evolve to a stationary state. These results suggest that the moving puncture technique should be viewed as a type of ''natural excision.''.
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.
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.
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.)
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.
121456313
A low energy bound atomic electron Compton scattering model for Geant4
Abstract A two-body fully relativistic three-dimensional scattering framework has been utilised to develop an alternative Compton scattering computational model to those adapted from Ribberfors’ work for Monte Carlo modelling of Compton scattering. Using a theoretical foundation that ensures the conservation of energy and momentum in the relativistic impulse approximation, this new model, the Monash University Compton scattering model, develops energy and directional algorithms for both the scattered photon and ejected Compton electron from first principles. The Monash University Compton scattering model was developed to address the limitation of the Compton electron directionality algorithms of other computational models adapted from Ribberfors’ work. Here the development of the Monash University Compton scattering model, including its implementation in a Geant4 low energy electromagnetic physics class, G4LowEPComptonModel, is outlined. Assessment of the performance of G4LowEPComptonModel was undertaken in two steps: (1) comparison with respect to the two standard Compton scattering classes of Geant4 version 9.5, G4LivermoreComptonModel and G4PenelopeComptonModel, and (2) experimental comparison with respect to Compton electron kinetic energy spectra obtained from the Compton scattering of 662 keV photons off the K-shell of gold. Both studies illustrate that the Monash University Compton scattering model, and in turn G4LowEPComptonModel, is a viable replacement for the majority of computational models that have been adapted from Ribberfors’ work. It was also shown that the Monash University Compton scattering model is able to reproduce the Compton scattering triply differential cross-section Compton electron kinetic energy spectra of 662 keV photons K-shell scattering off of gold to within experimental uncertainty.