Here we describe one such ADM method T2 that Texas and Syracuse are working on.
The evolution equations that the T2 solves are as follows:
where 
is the 3-metric,
is the extrinsic curvature,
is the covariant derivative computational with 
,
is the lapse function, 
is the shift vector
and 
is the Lie
derivative along the vector field 
.
is given
by the following equation:
