69 research outputs found
The non-isentropic Einstein-Euler system written in a symmetric hyperbolic form
We cast the non--isentropic Einstein--Euler system into a symmetric
hyperbolic form. Such systems are very suited to treat initial value problems
of hyperbolic type. We obtain this form by using the pressure and not the
density as a variable. However, the system becomes degenerate when the
pressure approaches zero, and in these cases we regularise the system by
replacing the pressure with an appropriate new matter variable, the Makino
variable
Trapped surfaces in spherical expanding open universes
Consider spherically symmetric initial data for a cosmology which, in the
large, approximates an open Friedmann-Lema{\^\i}tre
universe. Further assume that the data is chosen so that the trace of the
extrinsic curvature is a constant and that the matter field is at rest at this
instant of time. One expects that no trapped surfaces appear in the data if no
significant clump of excess matter is to be found. This letter confirms this
belief by displaying a necessary condition for the existence of trapped
surfaces.This necessary condition, simply stated, says that a relatively large
amount of excess matter must be concentrated in a small volume for trapped
surfaces to appear.Comment: 8 pages, Late
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