Black Holes: Classical Properties, Thermodynamics and Heuristic Quantization

I start with a discussion of the no-hair principle. The hairy black hole solutions of recent vintage do not deprive it of value because they are often unstable. Generic properties of spherical static black holes with nonvacuum exteriors are derived. These form the basis for the discussion of the new no scalar hair theorems. I discuss the generic phenomenon of superradiance for its own sake, as well as background for black hole superradiance. First I go into uniform linear motion superradiance with some examples. I then discuss Kerr black hole superradiance in connection with a general rotational superradiance theory with possible applications in the laboratory. Adiabatic invariants have played a weighty role in theoretical physics. I explain why the horizon area of a nearly stationary black hole can be regarded as an adiabatic invariant, and support this by examples as well as a general discussion of perturbations of the horizon. The horizon area’s adiabatic invariance suggests that its quantum counterpart is quantized in multiples of a basic unit. Consideration of the quantum analog of the Christodoulou reversible processes provides support for this idea. Area quantization provides a definite discrete black hole mass spectrum. Black hole spectroscopy follows: the Hawking semiclassical spectrum is replaced by a spectrum of nearly uniformly spaced lines whose envelope may be roughly Planckian. I estimate the lines’ natural broadening. To check on the possibility of line splitting, I present a simple algebra involving, among other operators, the black hole observables. Under simple assumptions it also leads to the uniformly spaced area spectrum. In these lectures I take units for which c = 1. Occasionally, where mentioned explicitly, I also set G = 1, but