Plane waves in quantum gravity: Breakdown of the classical spacetime - art. no. 084019

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearl y polarized plane waves in vacuum gravity. This model has no constraints an d its degrees of freedom can be interpreted as an infinite and continuous s et of annihilation and creation like variables. We also consider a simplifi ed version of the model, in which the number of modes is restricted to a di screte set. In both cases, the quantization is achieved by introducing a Fo ck representation. We find regularized operators to represent the metric an d discuss whether the coherent states of the quantum theory are peaked arou nd classical spacetimes. It is shown that, although the expectation value o f the metric on Killing orbits coincides with a classical solution, its rel ative fluctuations become significant when one approaches a region where nu ll geodesics are focused. In that region, the spacetimes described by coher ent states fail to admit an approximate classical description. This result applies as well to the vacuum of the theory.