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Contents
Contents
Stringy Black Holes
Martijn Derix
and
Jan Pieter van der Schaar
Contents
Introduction
General Relativity
Black Holes
Spherical symmetry
Schwarzschild solution
Reissner-Nordstrøm solution
Black Hole Physics
String Effective Actions
Classical String Theory
Low Energy String Effective Action
Kaluza Klein Theory
Reduction of the Low Energy String Effective Action
Four-dimensional Actions and Dual Symmetries
Reduction of
SEA
Dual Representation of the Axion
-Duality in Four Dimensions
Electric/Magnetic Duality
Duality in Electromagnetism
Generalized Electromagnetic Duality
-Duality with Two Vector Fields
Manifest
Invariant Action
Black Hole Solutions of String Effective Action
Equations of Motion
Dilaton Black Holes
One Vector Field
Two Vector Fields
Properties
Dilaton-Modulus solution
Axion Black Holes
Asymptotic Behaviour of Dilaton-Axion Solution
Dilaton-Axion Black Holes
Modulus-Dilaton-Axion Black Holes
Extremal Black Holes
Extremal RN Black Hole
Extremal Dilaton Solutions
Singly Charged Solution
Dyonic Solution
Dilaton-Modulus Extremal Solution
Solution Generating Techniques
Dimensional Reduction to Three Dimensions
Symmetry Group
Direct Reduction
Solution Generating Transformations
Symmetry Group
Dualisation of the vectors
Solution Generating Transformations
The General Solution
Extention to the Full SEA
Summary and Conclusions
Useful Tensors in Curved Space-Time
Tetrad Formalism
Levi-Civita Symbol in Curved Space-Time
The Symmetry Group O(d,d')
Overview of Solutions
Overview of Extremal Solutions
Bibliography
About this document ...
Jan Pieter van de Schaar 2005-09-09
SEA
-Duality in Four Dimensions
Invariant Action
-Duality with Two Vector Fields