The Interaction Of Outgoing And Ingoing Spherically Symmetric Null Fluids

Using similarity methods, the Einstein field equations coupled to two oppositely directed null fluids for a spherically symmetric space-time are reduced to an autonomous system of three ordinary differential equations. The space of solutions is studied in some detail and solutions are found that represent: (i) the backscattering of an initially outgoing thick null fluid shell in a background gravitational field with a central naked singularity, (ii) the formation of strong space-time singularities by the interaction of thick null fluid shells, (iii) the interaction of a core of null radiation with an incoming shell of null fluid, and (iv) cosmological models of Kantowski-Sachs type with initial and final singularities clothed by apparent horizons. © 1995 American Institute of Physics.3673663367

Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components--the ingoing and outgoing dusts--are assumed to interact only through gravitation. Different kinds of singularities, naked or "clothed", that can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bicak and Kuchar is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).Comment: 15 pages, 3 figures, submitted to Phys. Rev.

Laurent Expansions For Certain Functions Defined By Dirichlet Series

The Poisson summation formula is employed to find the Laurent expansions of the Dirichlet series F(s, c) = Σn = 0∞ exp[-(n + c)1/2s] and G(s, c) = Σn = 0∞(-1)n exp[-(n + c)1/2s] (0≤c<1) about s = 0. The Laurent expansions of F(s, c) and G(s, c) are convergent respectively for 0 < |s| < ∞ and |s| < ∞, and define the analytic continuation of the Dirichlet series to the half-plane Re s < 0. © 1993 Birkhäuser Verlag.451626

Cauchy-characteristic Evolution And Waveforms

We investigate a new methodology for the computation of waves generated by isolated sources. This approach consists of a global spacetime evolution algorithm based on a Cauchy initial-value formulation in a bounded interior region and based on characteristic hypersurfaces in the exterior; we match the two schemes at their common interface. The characteristic formulation allows accurate description of radiative infinity in a compactified finite coordinate interval, so that our numerical solution extends to infinity and accurately models the free-space problem. The matching interface need not be situated far from the sources, the wavefronts may have arbitrary nonspherical geometry, and strong nonlinearity may be present in both the interior and the exterior regions. Stability and second-order convergence of the algorithms (to the exact solution of the infinite-domain problem) are established numerically in three space dimensions. The matching algorithm is compared with examples of both local and nonlocal radiation boundary conditions proposed in the literature. For linear problems, matching outperformed the local radiation conditions chosen for testing, and was about as accurate (for the same grid resolution) as the exact nonlocal conditions. However, since the computational cost of the nonlocal conditions is many times that of matching, this algorithm may be used with higher grid resolutions, yielding a significantly higher final accuracy. For strongly nonlinear problems, matching was significantly more accurate than all other methods tested. This seems to be due to the fact that currently available local and nonlocal conditions are based on linearizing the governing equations in the far field, while matching consistently takes nonlinearity into account in both interior and exterior regions. © 1997 Academic Press.1361140167Lindman, E., (1975) J. Comput. Phys., 18, p. 66Israeli, M., Orszag, S.A., (1981) J. 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