Stimulated emission of radiation and the black hole information problem

Abstract

The quantum theory of black holes has opened up a window to study the intersection of general relativity and quantum field theory, but perceived paradoxes concerning the fate of classical information directed at a black hole horizon, as well as concerning the unitarity of the evaporation process, have led researchers to question the very foundations of physics. In this pedagogical review I clarify the ramifications of the fact that black holes not only emit radiation spontaneously, but also respond to infalling matter and radiation by emitting approximate clones of those fields in a stimulated manner. I review early purely statistical arguments based on Einstein’s treatment of black bodies, and then show that the Holevo capacity of the black hole (the capacity to transmit classical information through a quantum channel) is always positive. I then show how stimulated emission turns the black hole into an almost optimal quantum cloning machine, and furthermore discuss the capacity of black holes to transmit quantum information. Taking advantage of an analogy between black hole physics and non-linear optics I show that a calculation of the evolution of a black hole over time, using a discretization of the black hole $S$-matrix path integral, yields well-behaved Page curves suggesting that black hole evaporation is unitary. Finally, I speculate about possible observable consequences of stimulated emission of radiation in black holes.