Evaporation of two-dimensional black holes

Abstract

We present a detailed analysis of results from a new study of the quantum evaporation of CallanGiddings-Harvey-Strominger (CGHS) black holes within the mean field approximation. This semiclassical 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, I + R , 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 I + R 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.

Exploring New Physics Frontiers Through Numerical Relativity

“…In D = 2 a BH spacetime was obtained by Callan, Giddings, Harvey and Strominger (the CGHS BH), by considering GR non-minimally coupled to a scalar field theory [156]. This solution provides a simple, tractable toy model for numerical investigations of dynamical properties; for instance see [55, 54] for a numerical study of the evaporation of these BHs.Changing the equations: Different matter fields and higher curvature gravity.The uniqueness theorems of four-dimensional electrovacuum GR make clear that BHs are selective objects. Their equilibrium state only accommodates a specific gravitational field, as is clear, for instance, from its constrained multipolar structure.…”

“…In D = 2 a BH spacetime was obtained by Callan, Giddings, Harvey and Strominger (the CGHS BH), by considering GR non-minimally coupled to a scalar field theory [156]. This solution provides a simple, tractable toy model for numerical investigations of dynamical properties; for instance see [55, 54] for a numerical study of the evaporation of these BHs.…”

Black Hole Evaporation: A Perspective from Loop Quantum Gravity

“…First, the Hawking radiation starts (in earnest) precisely at the (retarded) instant of time at which the T-DH has maximum area. Second, as the evaporation proceeds, the area of the T-DH at any time instant is directly related to the Bondi mass at the corresponding retarded time instant at I + [33][34][35][36].…”

“…(b) Artist's depiction of a semi-classical Callen-Giddings-Harvey-Strominger (CGHS) black hole that was analyzed in detail in [34,35]. A Delta-distribution pulse of a scalar field from I − would lead to a black hole in the classical theory.…”

Black hole evaporation: information loss but no paradox

“…In the last twenty years, this model has often been referred toas a "laboratory for testing general ideas on more realistic black holes" (see [38], [39], [40] for reviews and the monograph [41]). Particularly, it has been extensively studied to incorporate back reaction effects due to quantum matter fields [42][43][44], building a toy model for quantum gravity [45,46], and also shading light on the information loss paradox [17,44]. We will follow this tradition and use it as a laboratory for testing our ideas about the resolution of the BHIP.…”