Strings Next To and Inside Black Holes

Abstract

The string equations of motion and constraints are solved near the horizon and near the singularity of a Schwarzschild black hole. In a conformal gauge such that $τ= 0$ ($τ$ = worldsheet time coordinate) corresponds to the horizon ($r=1$) or to the black hole singularity ($r=0$), the string coordinates express in power series in $τ$ near the horizon and in power series in $τ^{1/5}$ around $r=0$. We compute the string invariant size and the string energy-momentum tensor. Near the horizon both are finite and analytic. Near the black hole singularity, the string size, the string energy and the transverse pressures (in the angular directions) tend to infinity as $r^{-1}$. To leading order near $r=0$, the string behaves as two dimensional radiation. This two spatial dimensions are describing the $S^2$ sphere in the Schwarzschild manifold.