COSMIC WALLS FROM GRAVITATIONAL COLLAPSE

The formation of plane cosmic walls of negligible thickness from the collapse of smooth inhomogeneous plane-symmetric distributions of matter is considered. Two models with different asymptotic behaviors far from the wall in formation are constructed. In the first, the fluid far from the wall is anisotropic, with pressures proportional to density. The second model describes an asymptotically isotropic ideal gas in isentropic flow. Even though both models start from matter distributions with positive density and pressures everywhere, it is found that, during the collapse, negative pressures (tensions) appear within the wall in formation.49126500651

THE INTERACTION OF OUTGOING AND INGOING SPHERICALLY SYMMETRICAL 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 held 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. (C) 1995 American Institute of Physics.3673663367

ASYMPTOTIC SUMMATION OF HERMITE SERIES

A new method for the numerical evaluation of slowly convergent or even divergent series involving the Hermite functions psi(m)(x) = (2(m)m! square-root pi)-1/2 e-x2/2H(m)(x) is presented. We consider series with either of the forms F(x) = SIGMA(m = o) infinity c(m)psi(m)(x/square-root 2) and G(x, y) = SIGMA(m = o) infinity c(m)psi(m)(x/square-root 2)psi(m)(y/square-root 2), where c(m) decays algebraically as m --> infinity. The first series is a Fourier-Hermite series, while the second arises in the representation of Green functions for problems whose eigenfunctions involve the Hermite functions. By use of the Poisson summation formula, we derive rapidly convergent asymptotic expansions for the remainders of these series after a sufficiently large number of terms. The series can then be evaluated as a partial sum plus an asymptotic approximation to its remainder. The asymptotic expansion for the remainder of G(x,y) also reveals the nature of the possible singular behaviour of this series near x = y.25490992

COSMIC LOOPS AND BUBBLES IN EXPANDING UNIVERSES

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Cauchy-characteristic matching: A new approach to radiation boundary conditions

We investigate a new methodology for computing wave generation, using Cauchy evolution in a bounded interior region and characteristic evolution in the exterior. Matching the two schemes eliminates usual difficulties such as backreflection from the outer computational boundary. Mapping radiative infinity into a finite grid domain allows a global solution. The matching interface can be close to the sources, the wave fronts can have arbitrary geometry, and strong nonlinearity can be present. The matching algorithm dramatically outperforms traditional radiation boundary conditions.76234303430