Quantum Singularities Around a Global Monopole

The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator are found and their importance to the quantum interpretation of singularities is emphasized.Comment: 5 pages, revte

Properties of four numerical schemes applied to a scalar nonlinear scalar wave equation with a GR-type nonlinearity

We study stability, dispersion and dissipation properties of four numerical schemes (Iterative Crank-Nicolson, 3'rd and 4'th order Runge-Kutta and Courant-Fredrichs-Levy Non-linear). By use of a Von Neumann analysis we study the schemes applied to a scalar linear wave equation as well as a scalar non-linear wave equation with a type of non-linearity present in GR-equations. Numerical testing is done to verify analytic results. We find that the method of lines (MOL) schemes are the most dispersive and dissipative schemes. The Courant-Fredrichs-Levy Non-linear (CFLN) scheme is most accurate and least dispersive and dissipative, but the absence of dissipation at Nyquist frequency, if fact, puts it at a disadvantage in numerical simulation. Overall, the 4'th order Runge-Kutta scheme, which has the least amount of dissipation among the MOL schemes, seems to be the most suitable compromise between the overall accuracy and damping at short wavelengths.Comment: 9 pages, 8 Postscript figure

One-dimensional nuclear dynamics in the time-dependent Hartree-Fock approximation

The time-dependent Hartree-Fock theory is applied to the large amplitude dynamics of slabs of spin and isospin symmetric nuclear matter. The slabs are translationally invariant in two transverse dimensions, and with the simplified effective interaction used in this work, the problem is reduced to a set of coupled nonlinear equations for time-dependent functions of a single spatial variable. By specification of appropriate initial conditions, large amplitude oscillations of a single slab, the scattering of a slab from an external potential barrier, and collisions of two slabs have been investigated. The results evidence a wide variety of dynamic phenomena, including fusion, compound nucleus formation, dissipation, strongly damped collisions, shock wave propagation, and fragmentation. The microscopic aspects of the dynamics, the relation to fluid mechanics, and the practical and conceptual problems arising from the theory are discussed in detail