  When probed with conformally invariant matter fields, light cones in
Minkowski spacetime satisfy thermodynamical relations which are the analog of
those satisfied by stationary black holes coupled to standard matter fields.
These properties stem from the fact that light cones are conformal Killing
horizons stationary with respect to observers following the radial conformal
Killing fields in flat spacetime. The four laws of light cone thermodynamics
relate notions such as (conformal) temperature, (conformal) surface gravity,
(conformal) energy and a conformally invariant notion related to area change.
These quantities do not admit a direct physical interpretation in flat
spacetime. However, they become the usual thermodynamical quantities when
Minkowski is mapped, via a Weyl transformation, to a target spacetime where the
conformal Killing field becomes a proper Killing field. In this paper we study
the properties of such spacetimes. The simplest realisation turns out to be the
Bertotti-Robinson solution, which is known to encode the near horizon geometry
of near extremal and extremal charged black holes. The analogy between light
cones in flat space and black hole horizons is therefore strengthened. The
construction works in arbitrary dimensions; in two dimensions one recovers the
Jackiv-Teitelboim black hole of dilaton gravity. Other interesting realisations
are also presented.
