Claudio Dappiaggi
(U Pavia)
Projecting massive scalar fields on null infinity: a step toward an holographic description
In the framework of asymptotically flat spacetimes, future null
infinity represents the natural codimension one submanifold where to
holographically encode data from a bulk field theory either at a classical and
at a quantum level. Such an idea can be implemented almost straightforwardly
for massless free fields though the problem is drastically more complicated in
the massive case. Even for real scalar fields it does not exist a way to
project smooth solutions of the Klein-Gordon equation for compactly supported
initial data into a smooth function over null infinity. Exploiting harmonic
analysis and Strichartz global norm estimates we propose a possible solution
to this problem at least in Minkowski spacetime. Eventually we discuss our
construction from the point of view of the holographic principle.
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