Evaporation of 2-Dimensional Black Holes

Abstract

We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes within the mean-field approximation. This semi-classical theory incorporates back reaction. Our analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. One of the anticipated properties we confirm is that the semi-classical space-time is asymptotically flat at right future null infinity, $\spr$, yet incomplete in the sense that null observers reach a future Cauchy horizon in finite affine time. Unexpected behavior includes that the Bondi mass traditionally used in the literature can become negative even when the area of the horizon is macroscopic; an improved Bondi mass remains positive until the end of semi-classical evaporation, yet the final value can be arbitrarily large relative to the Planck mass; and the flux of the quantum radiation at $\spr$ is non-thermal even when the horizon area is large compared to the Planck scale. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties. Although the literature on CGHS black holes is quite rich, these features had escaped previous analyses, in part because of lack of required numerical precision, and in part due to misinterpretation of certain properties and symmetries of the model. Finally, our results provide support for the full quantum scenario recently developed by Ashtekar, Taveras and Varadarajan, and also offer a number of interesting problems to the mathematical relativity and geometric analysis communities.