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

Jay R. Yablon 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?
$$ No.
I am speaking of analytical solutions where the differential
equations are solved exactly, *not* numerical approximations.
$$ YABsolutely no.

Maxwell's energy tensor of electrodynamics
T^u_v = (1/4pi) [F^ut F_vt - (1/4) lambda^u_v F^st F_st].

-=- ..interested in solutions where F^uv_u=0 (free space)
-=- ..and 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.
--Jay R Yablon.
To be clear, I am *not* looking for solutions where the metric
is assumed to be a Minkowski metric. Lots of analyses assume
a flat-space background for electrodynamics.

Rather, I am looking for *exact* solutions, to the extent that
such solutions are known, which derive a curved spacetime
metric from the electromagnetic field strength tensor, that is,
which derive g_uv = g_uv(F^uv) via the Maxwell tensor T^u_v,
whereby T^u_v(g_uv, F_uv) simply becomes T^u_v(F_uv) once the
g_uv(F^uv) are found.

$$ Maxwell used REAL "flat" plates in air to derive his equations.
$$ This is why GR is only "approximately" flat, at-great-distance.
$$ Even a dot has extreme "curvature", so you can imagine a point.
$$ GR is a "point-SURFACE manifold" at the end of it's WORLD-line.
$$ This is why GR is NOT a "local" theory (where it's all Newton).
$$ This is why GR is a "far-field" theory (where it's all Newton).
$$ [ The "SURFACE" of a GR-"POiNT" is "FLAT-at-a-GREAT-distance ].
$$
$$ Tom R ought derive a set from lab work ..using "CURVED" plates.
$$ [Just let the PLATEs be M1 and m1 and the air as the "AEther"].
$$
$$ Hope this helps, ```Brian A M Stuckless, Ph.T (Tivity).
GR CUT OFF it's own WORLD-line, having DECLARED no PRiOR geometry.
p.s. A GR-"geodesic" is *NOT* Uncle Al's "OTHER LONGER way round".

Thanks. Jay R. Yablon Email:
Solution to Einstein's Field Equations where T^uv not= 0?.