# Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states

April 18, 2014

We discuss the quantization of linearized gravity on globally hyperbolic,
asymptotically flat, vacuum spacetimes and the construction of distinguished
states which are both of Hadamard form and invariant under the action of all
bulk isometries. The procedure, we follow, consists of looking for a
realization of the observables of the theory as a sub-algebra of an auxiliary,
non-dynamical algebra constructed on future null infinity $\Im^+$. The
applicability of this scheme is tantamount to proving that a solution of the
equations of motion for linearized gravity can be extended smoothly to $\Im^+$.
This has been claimed to be possible provided that a suitable gauge fixing
condition, first written by Geroch and Xanthopoulos, is imposed. We review its
definition critically showing that there exists a previously unnoticed
obstruction in its implementation leading us to introducing the concept of
radiative observables. These constitute an algebra for which a Hadamard state
induced from null infinity and invariant under the action of all spacetime
isometries exists and it is explicitly constructed.

Keywords:

QFT on curved spacetimes, linearized gravity