The embedding of Minkowski space into the Einstein cylinder
.
The conformal diagram of Minkowski space.
Spacelike hypersurfaces in the conformal picture.
Waveforms in physical space-time.
Waveforms in conformal space-time.
The physical scenario: The figure describes the geometry of an isolated system. Initial data are prescribed on the blue parts, i.e. on a hyperboloidal hypersurface and the part of
which is in
its future. Note that the two cones
and 
are separated to indicate the
non-trivial transition between
them.
The geometry of the asymptotic characteristic initial value problem: Characteristic data are given on the blue parts, i.e. an ingoing null surface and the part of
that is in its future.
Note that the ingoing surface may
develop self-intersections and caustics.
The geometry near space-like infinity: The “point”
has been blown up to
a cylinder that is attached to
and 
. The physical space-time is
the exterior part of this “stovepipe”. The “spheres” 
and 
are shown in blue and light green, respectively.
The brown struts symbolize the
conformal geodesics used to set up the construction. Note that they
intersect 
and continue into the unphysical part.
The geometry of the standard Cauchy approach. The green lines are surfaces of constant time. The blue line indicates the outer boundary.
The geometry of Cauchy-Characteristic matching. The blue line indicates the interface between the (inner) Cauchy part and the (outer) characteristic part.
The geometry of the conformal approach. The green lines indicate the foliation of the conformal manifold by hyperboloidal hypersurfaces.
An axi-symmetric solution of the Yamabe equation with
on the boundary
(top) and its third differences in
the 
-direction (bottom). The location of 
is clearly visible.
The difference between two solutions of the Yamabe equation obtained with different boundary conditions outside. Only the values less than
are shown.
Upper corner of a space-time with singularity (thick line). The dashed line is
, while the thin line
is the locus of vanishing divergence of outgoing light rays,
i.e. an apparent
horizon.
Decay of the radiation at null-infinity.
The radiation field
and the Bondi mass for a radiating A3-like
space-time.
The numerically generated ‘Kruskal diagram’ for the Schwarzschild solution.
The rescaled Weyl tensor in a flat space-time obtained from flat initial data and random boundary data in the unphysical region.
