Interacting quantum fields around a black hole

If one studies interacting fields on a black hole background using ordinary Feynman diagrams, one is faced with a problem of what to do with lines that cross the horizon. To avoid this difficulty a formulation is developed which can be expressed graphically in terms of a new class of diagram with external lines only at infinity. This formalism is applied to study the question of whether spontaneously broken symmetry would be restored near the black hole. It is also used to show that a black hole can emit more particles than antiparticles even in theories where the particle number is locally conserved by a globalU(1) symmetry.