A "black hole theorem," and its implications

A "black hole theorem" is stated, exhibiting the basic conflict of the information problem. This is formulated in a more general context than that of quantum field theory on a background, and is based on describing a black hole as a quantum subsystem of a larger system, including its environment. As with the Coleman-Mandula theorem, the most important point is probably the loophole in the "theorem," and what this tells us about the fundamental structure of quantum gravity. This "theorem" in particular connects to the general question of how to define quantum subsystems in quantum gravity. If black holes do behave as quantum subsystems, at least to a good approximation, evolve unitarily, and do not leave remnants, the "theorem" implies the presence of interactions between a black hole and its environment that go beyond a description based on local quantum fields. These can be parameterized in a principled way, and with motivated additional assumptions indicate possible observational signatures, which can be investigated by electromagnetic or gravitational wave observations of black holes.