  We demonstrate the existence of quantum hair in electrodynamics and gravity
using effective action techniques. In the case of electrodynamics we use the
Euler-Heisenberg effective action while in the case of quantum gravity we use
the unique effective action. We give a general formulation of these effects
which applies to both theories and discuss analogies and differences between
them. Furthermore, we present a QED analog to black hole evaporation.
Spontaneous pair production in the external field of a ball of charge is
analogous to Hawking radiation from black holes. Assuming spherical symmetry,
the Gauss law prevents the external field from depending on the density profile
of the ball. Quantum corrections violate these expectations, showing that
quantum radiation can encode classically forbidden information about the
source.
