Partner particles for moving mirror radiation and black hole evaporation

Abstract

The partner mode with respect to a vacuum state for a given mode (like that corresponding to one of the thermal particles emitted by a black hole) is defined and calculated. The partner modes are explicitly calculated for a number of cases, in particular for the modes corresponding to a particle detector being excited by turn-on/turn-off transients, or with the thermal particles emitted by the accelerated mirror model for black hole evaporation. One of the key results is that the partner mode in general is just a vacuum fluctuation, and one can have the partner mode be located in a region where the state cannot be distinguished from the vacuum state by any series of local measurements, including the energy density. For example, ``information'' (the correlations with the thermal emissions) need not be associated with any energy transport. The idea that black holes emit huge amounts of energy in their last stages because of all the information which must be emitted under the assumption of black hole unitarity is found to not necessarily be the case.