Speaker
Juan A Valiente
(Queen Mary, London)
Description
H. Friedrich has shown that if one considers a time symmetric initial
data set for the Einstein vacuum equations admitting an analytic
compactification at infinity, then necessary conditions for the
solutions to the transport system implied by the conformal Einstein
equations at the cylinder at spatial infinity to extend smoothly to
the critical sets where null infinity touches spatial infinity is that
the Cotton-Bach tensor of the conformal metric, and its trace-free
symmetrised higher order derivatives vanish at spatial infinity.
In this talk the generalisation of this regularity condition to data
with non-vanishing second fundamental forms is examined. It is
discussed how these regularity conditions can be phrased in terms of
the vanishing at infinity of a pair of tensors and their higher order
symmetrised derivatives. It is shown that these "generalised
regularity conditions" are only a restriction on the freely specifiable
data. The relation of these "generalised regularity conditions" to
stationary data is considered. Finally, it is also discussed how these
regularity conditions can be used to construct purely radiative data
at "past null infinity".
