Squeezed States in BlackHole Evaporation by Analytic Continuation
Abstract
We compute the semiclassical quantum amplitude to go from an initial spherically symmetric bosonic matter and gravitational field configuration to a final radiation configuration, corresponding to the relic Hawking radiation from a nonrotating, chargeless black hole which evaporates completely. This is obtained via the classical action integral which is solely a boundary term. On discretising the classical action, the quantum amplitude can be expressed in terms of generalised coherent states of the harmonic oscillator. A squeezedstate representation is obtained by complexifying the proper time separation T at spatial infinity between the initial and final spacelike hypersurfaces. Such a procedure is deemed necessary as the twosurface problem for Dirichlet boundary data and wavelike perturbations is not well posed. We find that infinitesimal rotation into the lower complex T plane is equivalent to a highlysqueezed final state for the relic radiation, similar to the relic gravitationalwave background in cosmology. This final state is a pure state, and so the unpredictability associated with the final momentarilynaked singularity is avoided. The cosmological analogy is the tunnelling from an initial smooth Euclidean or timeless state to a classical universe. The highsqueezing limit corresponds to a final state of the Hawking flux which is indistinguishable from a stochastic collection of standing waves. The phases conjugate to the field amplitudes are squeezed to discrete values. We also discuss the entropy of the final radiation in the highsqueezing limit.
 Publication:

arXiv eprints
 Pub Date:
 September 2002
 arXiv:
 arXiv:grqc/0209113
 Bibcode:
 2002gr.qc.....9113F
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 25 pages, 1 figure