Re: Solution to Einstein's Field Equations where T^uv not= 0?

Jay R. Yablon <jyablon@xxxxxxxxxxxx> wrote:
Many of the widely-studied solutions to Einstein's field equations are taken
in vacuo, that is, at events where the energy momentum tensor T^uv=0. This
includes Schwarzchild and Kerr geometries, for example.

Have there been many exact solutions found where T^uv not= 0? I am speaking
of analytical solutions where the differential equations are solved exactly,
*not* numerical approximations.

I am especially interested in any exact solutions based on the usual Maxwell
energy tensor of electrodynamics T^u_v = (1/4pi) [F^ut F_vt - (1/4)
lambda^u_v F^st F_st]. I am interested in solutions both where F^uv_u=0
(free space) and also where F^uv_u=J^v (space with current sources).
Conditions of interest include static spherical symmetry in the nature of
Schwarzchild, and rotation with spherical symmetry about the z-axis in the
nature of Kerr.

You might find gr-qc/0604108 of interest:
Title: Neutral perfect fluids and charged thin shells
with electromagnetic mass in general relativity
Authors: Victor Varela
Abstract:
We build extended sources for the Reissner-Nordstr\"{o}m metric. Our
models describe a neutral perfect fluid core bounded by a charged thin
shell, and feature everywhere positive rest mass density and everywhere
non-negative active gravitational mass, as well as classical electron
radius and electromagnetic total mass. We contrast our results with
previously discussed models featuring similar properties at the expense
of including anisotropic pressures within the fluid. Our charged
thin shells are restricted by the 2D texture equation of state which
causes the continuity of the active gravitational mass, in spite of the
singularity of the energy-momentum tensor. We mention possible extensions
of this study suggested by modified active mass formulae proposed in
the literature.

ciao,

--
-- "Jonathan Thornburg -- remove -animal to reply" <jthorn@xxxxxxxxxxxxxxxx>
Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
Golm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

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