Abstract
Black holes, first predicted two centuries ago, are a ubiquitous feature of modern gravitation theory. This volume reports the proceedings of a Spring School in 1998 which tried to give an almost encyclopaedic summary of black hole physics.
The Schwarzschild solution (1915) led on the one hand to an investigation of the gravitational collapse of stellar objects. Those with a mass less than about 1.4 solar masses can collapse to a stable state, a white dwarf, where gravity is balanced by the degeneracy pressure of free electrons. Heavier stars, whose mass is less than about three solar masses, can become neutron stars. Otherwise there is no stable configuration, and classical relativity predicts collapse to a gravitational singularity. The astrophysics of such objects is reviewed succinctly in this volume by Treves and Haardt. (Black holes are of interest in other astrophysical situations, e.g., active galactic nuclei, but that is not covered here, although useful references are given.) Although there are some exact solutions describing idealized models of gravitational collapse, it soon became clear that computers would be needed to describe realistic models, and from this origin has emerged the burgeoning subject of numerical relativity. Research in this area has bifurcated into the study of (a) the gravitational radiation produced by interacting black holes, which (hopefully) will become observable within a decade and (b) critical phenomena occurring in gravitational collapse, a concept discovered first numerically and which has so far eluded a complete theoretical explanation. The numerics of black holes are ably reviewed by Matzner in this volume.
Mathematical studies since 1915 have been no less intense. One can identify a classical (both literal and non-quantum) period before 1974, in which the mathematics of black hole exact solutions was worked out, culminating in the discovery of a striking resemblance between the laws of black hole mechanics and thermodynamics. In 1974 Hawking considered quantum fields propagating in a given classical black hole spacetime and discovered that external observers appear to see thermal radiation at a temperature proportional to 
Mfor a Schwarzschild black hole of mass M, which implies that the hole has an entropy proportional to M2. This raises a number of paradoxes whose resolution cannot be found within a semiclassical approach; a consistent theory of quantum gravity would appear to be necessary.
Three quarters of this book is devoted to that topic. First Kiefer reviews, compactly, black hole thermodynamics, Hawking radiation and its paradoxes, as well as black holes in canonical quantum gravity and in string theory. Next Dijkgraaf reviews in depth the five-dimensional Strominger-Vafa black hole model, which he claims is representative of `a microcosm of the ideas which permeate modern day string theory', looking at, inter alia, the D5-D1 brane system, matrix theory and near-horizon limits in anti-de Sitter string theory. The longest contribution, from D'Auria and Fré, is entitled `BPS black holes in supergravity: duality groups, p-branes, central charges and entropy', which is a reasonable summary of its content. The main goal is to classify Bogomolnyi-Prasad-Sommerfeld black hole solutions of four-dimensional supergravity and to elucidate the group-theoretical structure of black hole entropy.
Although these lectures were addressed to an audience `assumed to be mostly unfamiliar with supergravity and superstrings' (such as your reviewer), few concessions were made. In mitigation, expert guidance through the many review articles at different levels is offered.
For whom is this book intended? As I have indicated, there were two distinct themes running through the School. While everyone should read Kiefer's review, few will wish to pursue both directions. Since less than a quarter of the book is devoted to astrophysical and numerical aspects, readers interested in this material may prefer to consult a library copy. The quantum theoretical contributions are realistically intended for new or prospective research students, or for researchers looking to change fields. They may however be deterred by the price. Although the typesetting is immaculate (thanks to LaTeX) and the paper is good quality the binding does seem somewhat flimsy for £80.