  Minkowski space is a physically important space-time for which the finding an
adequate holographic description is an urgent problem. In this paper we develop
further the proposal made in hep-th/0303006 for the description as a duality
between Minkowski space-time and a Conformal Field Theory defined on the
boundary of the light-cone. We focus on the gravitational aspects of the
duality. Specifically, we identify the gravitational holographic data and
provide the way Minkowski space-time (understood in more general context as a
Ricci-flat space) is reconstructed from the data. In order to avoid the
complexity of non-linear Einstein equations we consider linear perturbations
and do the analysis for the perturbations. The analysis proceeds in two steps.
We first reduce the problem in Minkowski space to an infinite set of field
equations on de Sitter space one dimension lower. These equations are quite
remarkable: they describe massless and massive gravitons in de Sitter space. In
particular, the partially massless graviton appears naturally in this
reduction. In the second step we solve the graviton field equations and
identify the holographic boundary data. Finally, we consider the asymptotic
form of the black hole space-time and identify the way the information about
the mass of the static gravitational configuration is encoded in the
holographic data.
