We report a numerical evolution of axisymmetric Brill waves. The numerical algorithm has new features, including (i) a method for keeping the metric regular on the axis and (ii) the use of coordinates that bring spatial infinity to the edge of the computational grid. The dependence of the evolved metric on both the amplitude and shape of the initial data is found.Comment: added more discussion of results and several reference

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We perform numerical simulations of the gravitational collapse of a spherically symmetric scalar field. For those data that just barely do not form black holes we find the maximum curvature at the position of the central observer. We find a scaling relation between this maximum curvature and distance from the critical solution. The scaling relation is analogous to that found by Choptuik for black hole mass for those data that do collapse to form black holes. We also find a periodic wiggle in the scaling exponent.

We compare results from a relativistic and a nonrelativistic set of 2D axisymmetric jet simulations. For a set of five relativistic simulations that either increase the Lorentz factor or decrease the adiabatic index we compute nonrelativistic simulations with equal useful power or thrust. We examine these simulations for morphological and dynamical differences, focusing on the velocity field, the width of the cocoon, the age of the jets, and the internal structure of the jet itself.The primary result of these comparisons is that the velocity field of nonrelativistic jet simulations cannot be scaled up to give the spatial distribution of Lorentz factors seen in relativistic simulations. Since the local Lorentz factor plays a major role in determining the total intensity for parsec scale extragalactic jets, this suggests that a nonrelativistic simulation cannot yield the proper intensity distribution for a relativistic jet. Another general result is that each relativistic jet and its nonrelativistic equivalents have similar ages (in dynamical time units, ≡ R/a a , where R is the initial radius of a cylindrical jet and a a is the sound speed in the ambient medium). Also, jets with a larger Lorentz factor have a smaller cocoon size.

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