This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

Abstract. The procedure used recently by Hawking to demonstrate the creation of massless particles by black holes is applied to the Rindler coordinate system in flat space-time. The result is that an observer who undergoes a uniform acceleration K apparently sees a fixed surface radiate with a temperature of ~/27t. Some implications of this result are discussed.

We examine the modes of a scalar field in de Sitter space and construct quantum two-point functions. These are then used to compute a finite stress tensor by the technique of covariant point-splitting. We propose a renormalization ansatz based on the DeWitt-Schwinger expansion, and show that this removes all am biguities previously present in pointsplitting regularization. The results agree in detail with previous work by dimensional regularization, and give rise to an anomalous trace with the conventional coefficient. We describe how’ our treatment may be extended to more general situations.

%'e calculate the vacuum expectation value, T"", of the energy-momentum tensor of a massless scalar field in a general two-dimensional spacetime and evaluate it in a two-dimensional model of gravitational collapse. In two dimensions, quantum radiation production is incompatible with a conserved and traceless T"".We therefore resolve an ambiguity in our expression for T~", regularized by a geodesic point-separation procedure, by demanding conservation but allowing a trace. In the collapse model, the results support that picture of black-hole evaporation in which pairs of particles are created outside the horizon (and not entirely in the collapsing matter), one of which carries negative energy into the future horizon of the black hole, while the other contributes to the thermal flux at infinity.

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The energy-momentum tensor is calculated in the two dimensional quantum theory of a massless scalar field influenced by the motion of a perfectly reflecting boundary (mirror). This simple model system evidently can provide insight into more sophisticated processes, such as particle production in cosmological models and exploding black holes. In spite of the conformally static nature of the problem, the vacuum expectation value of the tensor for an arbitrary mirror trajectory exhibits a non-vanishing radiation flux (which may be readily computed). The expectation value of the instantaneous energy flux is negative when the proper acceleration of the mirror is increasing, but the total energy radiated during a bounded mirror motion is positive. A uniformly accelerating mirror does not radiate; however, our quantization does not coincide with the treatment of that system as a ‘static universe’. The calculation of the expectation value requires a regularization procedure of covariant separation of points (in products of field operators) along time-like geodesics; more naïve methods do not yield the same answers. A striking example involving two mirrors clarifies the significance of the conformal anomaly.

I n spite of the fundamental difficulties associated with the thermodynamics of self-gravitating systems, the objects known as black holes appear to conform to a very straightforward generalisation of standard laboratory thermodynamics. I n this review the generalised theory is examined in detail. It is shown how familiar concepts such as temperature, entropy, specific heats, phase transitions and irreversibility apply to systems containing black holes, and some concrete results of the theory are presented. The thermodynamic connection is based on Hawking's celebrated application of quantum theory to black holes, and in this review the quantum aspects are described in detail from several standpoints, both heuristic and otherwise. The precise mechanism by which the black hole produces thermal radiation, its nature and origin, and the energetics of back-reaction on the hole are reviewed. The thermal states of quantum holes are also treated using the theory of thermal Green functions, and the entropy of the hole is shown to be related to the loss of information about the quantum states hidden behind the event horizon. Some related topics such as accelerated mirrors and observers in Minkowski space, super-radiance from rotating holes and the thermodynamics of general self-gravitating systems are also briefly discussed.

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