  As is well-known, Newton's gravitational theory can be formulated as a
four-dimensional space-time theory and follows as singular limit from
Einstein's theory, if the velocity of light tends to the infinity. Here
'singular' stands for the fact, that the limiting geometrical structure differs
from a regular Riemannian space-time. Geometrically, the transition Einstein to
Newton can be viewed as an 'opening' of the light cones. This picture suggests
that there might be other singular limits of Einstein's theory: Let all light
cones shrink and ultimately become part of a congruence of singular world
lines. The limiting structure may be considered as a nullhypersurface embedded
in a five-dimensional spacetime. While the velocity of light tends to zero
here, all other velocities tend to the velocity of light. Thus one may speak of
an ultrarelativistic limit of General Relativity. The resulting theory is as
simple as Newton's gravitational theory, with the basic difference, that
Newton's elliptic differential equation is replaced by essentially ordinary
differential equations, with derivatives tangent to the generators of the
singular congruence. The Galilei group is replaced by the Carroll group
introduced by L\'evy-Leblond. We suggest to study near ultrarelativistic
situations with a perturbational approach starting from the singular structure,
similar to post-Newtonian expansions in the $c \to \infty$ case.
