  We establish an analogy between superconductor-metal interfaces and the
quantum physics of a black hole, using the proximity effect. We show that the
metal-superconductor interface can be thought of as an event horizon and
Andreev reflection from the interface is analogous to the Hawking radiation in
black holes. We describe quantum information transfer in Andreev reflection
with a final state projection model similar to the Horowitz-Maldacena model for
black hole evaporation. We also propose the Andreev reflection-analogue of
Hayden and Preskill's description of a black hole final state, where the black
hole is described as an information mirror. The analogy between Crossed Andreev
Reflections and Einstein-Rosen bridges is discussed: our proposal gives a
precise mechanism for the apparent loss of quantum information in a black hole
by the process of nonlocal Andreev reflection, transferring the quantum
information through a wormhole and into another universe. Given these
established connections, we conjecture that the final quantum state of a black
hole is exactly the same as the ground state wavefunction of the
superconductor/superfluid in the Bardeen-Cooper-Schrieffer (BCS) theory of
superconductivity; in particular, the infalling matter and the infalling
Hawking quanta, described in the Horowitz-Maldacena model, forms a Cooper
pair-like singlet state inside the black hole. A black hole evaporating and
shrinking in size can be thought of as the analogue of Andreev reflection by a
hole where the superconductor loses a Cooper pair. Our model does not suffer
from the black hole information problem since Andreev reflection is unitary. We
also relate the thermodynamic properties of a black hole to that of a
superconductor, and propose an experiment which can demonstrate the negative
specific heat feature of black holes in a growing/evaporating condensate.
