Lectures on black hole quantum mechanics

The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the qu antum theory of black holes, especially in the context of string theory. No ne of these are reflected here. The concept of quantum hair, which is discu ssed at length in the lectures, is certainly of permanent interest, and I c ontinue to believe that in some generalised form it will prove central to t he whole question of how information is stored in black holes. The discussi on of scattering and emission modes from various classes of black holes cou ld be; substantially simplified using modern techniques, and from currently popular perspectives the choice of examples might look eccentric. On the o ther hand fashions have changed rapidly in the field, and the big questions as stated and addressed here, especially as formulated for "real" black ho les (nonextremal, in four-dimensional, asymptotically flat space-time, with supersymmetry broken), remain pertinent even as the tools to address them may evolve. The four lectures I gave at the school were based on two lengthy papers tha t have now been published "Black Holes as Elementary Particles," Nuclear Ph ysics B380, 447 (1992) and "Quantum Hair on Black Holes," Nuclear Physics B 378, 175 (1992). The unifying theme of this work is to help make plausible the possibility that black holes, although they are certainly unusual and e xtreme states of matter, may be susceptible to a description using concepts that are not fundamentally different from those we use in describing other sorts of quantum-mechanical matter. In the first two lectures I discussed dilaton black holes. The fact that ap parently innocuous changes in the "matter" action can drastically change th e properties of a black hole is already very significant: it indicates that the physical properties of small black holes cannot be discussed reliably in the abstract, but must be considered with due regard to the rest of phys ics. (The macroscopic properties of large black holes, in particular those of astrophysical interest, are presumably well described by the familiar Ei nstein-Maxwell action which governs the massless fields. Heavy fields will at most provide Yukawa tails to the field surrounding the hole.) I will sho w how perturbations may be set up and analyzed completely, and why doing th is is crucial for understanding the semiclassical physics of the hole inclu ding the Hawking radiation quantitatively. It will emerge that there is a c lass of dilaton black holes which behave as rather straightforward elementa ry particles. In the other two lectures I discussed the issue of hair on black holes, in particular the existence of hair associated with discrete gauge charges and its physical consequences. This hair is particularly interesting to analyz e because it is invisible classically and to all orders in (h) over bar. It s existence shows that black holes can have some "internal" quantum numbers in addition to their traditional classification by mass, charge, and angul ar momentum. The text that follows, follows the original papers closely.