10814443
Black hole entropy and the Hamiltonian formulation of diffeomorphism invariant theories.
Path integral methods are used to derive a general expression for the entropy of a black hole in a diffeomorphism invariant theory. The result, which depends on the variational derivative of the Lagrangian with respect to the Riemann tensor, agrees with the result obtained from Noether charge methods by Iyer and Wald. The method used here is based on the direct expression of the density of states as a path integral (the microcanonical functional integral). The analysis makes crucial use of the Hamiltonian form of the action. An algorithm for placing the action of a diffeomorphism invariant theory in Hamiltonian form is presented. Other path integral approaches to the derivation of black hole entropy include the Hilbert action surface term method and the conical deficit angle method. The relationships between these path integral methods are presented. \textcopyright{} 1995 The American Physical Society.
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.)
119326995
DYNAMICAL ROTATIONAL INSTABILITY AT LOW T/W
Dynamical instability is shown to occur in differentially rotating polytropes with N = 3.33 and T/|W| 0.14. This instability has a strong m = 1 mode, although the m = 2, 3, and 4 modes also appear. Such instability may allow a centrifugally hung core to begin collapsing to neutron star densities on a dynamical timescale. The gravitational radiation emitted by such unstable cores may be detectable with advanced ground-based detectors, such as LIGO-II. If the instability occurs in a supermassive star, it may produce gravitational radiation detectable by the space-based detector LISA.
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.
42904289
Numerical simulations with a first order BSSN formulation of Einstein's field equations
We present a new fully first-order strongly hyperbolic representation of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement, and, in particular, binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of Baumgarte-Shapiro-Shibata-Nakamura evolutions with very high accuracy numerical techniques, such as spectral collocation multidomain or discontinuous Galerkin methods.
34139540
Shape of the beta spectra in the A=14 system.
29372740
Strength functions and spreading widths of simple shell model configurations.
The exact solution of the many-body problem in the framework of the nuclear shell model with a realistic residual Hamiltonian makes it possible to study the fragmentation of simple configurations as a function of excitation energy and interaction strength. The analysis is performed for 839 states with quantum numbers {ital J}{sup {pi}}{ital T}=0{sup +}0 in a system of 12 valence particles within the {ital sd} shell. Our statistics allow us to establish the generic shape of the strength function in the region of strong mixing. For the realistic interaction, the strength function is close to Gaussian in the central part and has exponential wings. The spreading width is larger than predicted by the standard golden rule. At the artificially suppressed interaction strength, we recover the Breit-Wigner shape and the golden rule for the spreading width. The transition between these regimes agrees with theoretical considerations based on the idea of chaotic dynamics. {copyright} {ital 1996 The American Physical Society.}
39044560
Neutron halos in the Na isotopes.
The neutron and proton density distributions of the Na isotopes out to the proton and neutron drip lines are calculated in the spherical Hartree-Fock model with a wide variety of density-dependent Skyrme interactions. The results are compared to recent experimental data for the interaction cross sections and for the rms radii. We discuss the role of the deformed intruder states and the problems associated with predicting the location of the neutron drip line for this mass region. {copyright} {ital 1996 The American Physical Society.}
840289
Analysis of magnetic dipole transitions between sd-shell states.
Experimental values of magnetic dipole transition strengths between states of sd-shell (A = 17--39) nuclei are analyzed with one-body transition densities from complete-space 0d/sub 5/2/-1s/sub 1/2/-0d/sub 3/2/ shell-model wave functions in order to extract empirical values for the higher-order corrections to the model M1 operator. These corrections, or renormalizations, are obtained in terms of the values of the effective single-particle matrix elements which, when combined with the model transition densities, yield a minimum deviation of the model predictions for M1 strengths from a set of selected experimental values. A total of 250 experimental data are investigated. Confirmation that the particular realizations of shell-model wave functions employed in the analysis of the data yield adequate descriptions of the actual nuclear states, and that the set of experimental data provides a thorough and accurate sampling of the relevant phenomena, are prerequisites to obtaining meaningful results from this procedure. These issues are studied with a variety of tests of the internal consistency of the procedures used.
19689278
Diproton decay of nuclei on the proton drip line.
The process of direct two-proton decay of nuclei with {ital Z}=22--28 on the proton drip line is considered. On the basis of new 0{ital d}{sub 3/2}-0{ital f}{sub {ital f}/2} shell-model mass extrapolations, {sup 39}Ti, {sup 42}Cr, {sup 45}Fe, {sup 48}Ni, and {sup 49}Ni are found to be bound to single-proton decay but unbound to two-proton decay. New estimates of the spectroscopic factors and lifetimes have been made. The decays of {sup 39}Ti, {sup 45}Fe, and {sup 48}Ni are found to be promising for further experimental investigation.