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DFD1B505-5003-48A5-96B8-3801F104F899

# Les Houches Lectures on Black Holes

Andy Strominger
arXiv:hep-th/9501071

Submitted on 12 January 1995

## Abstract

Contents: 1. Introduction 2. Causal Structure and Penrose Diagrams: Minkowski Space; 1+1 Dimensional Minkowski Space; Schwarzchild Black Holes; Gravitational Collapse and the Vaidya Spacetimes; Event Horizons, Apparent Horizons, and Trapped Surfaces 3. Black Holes in Two Dimensions: General Relativity in the $S$-Wave Sector; Classical Dilaton Gravity; Eternal Black Holes; Coupling to Conformal Matter; Hawking Radiation and the Trace Anomaly; The Quantum State; Including the Back-Reaction; The Large $N$ Approximation; Conformal Invariance and Generalizations of Dilaton Gravity; The Soluble $RST$ Model 4. The Information Puzzle in Four Dimensions: Can the Information Come Out Before the Endpoint?; Low-Energy Effective Descriptions of the Planckian Endpoint; Remnants?; Information Destruction?; The Superposition Principle; Energy Conservation The New Rules; Superselection Sectors, $\alpha$-parameters, and the Restoration of Unitarity 5. Conclusions and Outlook

## Preprint

Comment: 70 pages, 18 figures. Lectures presented at the 1994 Les Houches Summer School Fluctuating Geometries in Statistical Mechanics and Field Theory.'' (also available at http://xxx.lanl.gov/lh94/ )

Subjects: High Energy Physics - Theory; Astrophysics; General Relativity and Quantum Cosmology