Classical Hair in String Theory I: General Formulation

TL;DR

This paper develops a canonical formalism for classical hair in string theory black holes, showing how extra-dimensional fields influence black hole properties and deriving an effective theory relating horizon variables to observable hair.

Contribution

It introduces a general formalism for classical hair in string theory black holes, connecting horizon variables with observable hair and analyzing their thermodynamic properties.

Findings

Effective reduced Hamiltonian for black hole hair

Formal identification of temperature and entropy

Application to Cvetic-Youm dyon solution

Abstract

We discuss why classical hair is desirable for the description of black holes, and show that it arises generically in a wide class of field theories involving extra dimensions. We develop the canonical formalism for theories with the matter content that arises in string theory. General covariance and duality are used to determine the form of surface terms. We derive an effective theory (reduced Hamiltonian) for the hair in terms of horizon variables. % accessible to an observer at infinity. Solution of the constraints expresses these variables in terms of hair accessible to an observer at infinity. We exhibit some general properties of the resulting theory, including a formal identification of the temperature and entropy. The Cveti\v{c}-Youm dyon is described in some detail, as an important example.