Size and Shape of Rotating Strings and the Correspondence to Black Holes

TL;DR

This paper investigates the sizes of rotating strings across different angular momenta and compares them to rotating black holes, revealing similarities at low spins and differences at high spins, supported by a new random-walk model.

Contribution

It introduces a comparison of rotating string sizes with black holes across spin regimes and proposes a random-walk model for highly excited strings.

Findings

Size ratios are adiabatic invariants and comparable at low spins.

At high spins, string and black hole sizes diverge, reflecting the lack of correspondence.

A new random-walk model accurately predicts string sizes for all angular momenta.

Abstract

In light of the correspondence between black holes and fundamental strings with non-zero spin, we compute the sizes of rotating strings for small, moderate, and large values of the angular momentum and compare them to the sizes of rotating black holes. We argue that the ratio of the size perpendicular to the rotation plane to the size along the rotation plane is an approximate adiabatic invariant and can therefore be meaningfully compared for objects on different sides of the correspondence point. We show that the spin-dependence of this ratio for small angular momenta agrees for black holes and strings. When the spin is large, the ratios for these objects exhibit different behavior, but this is expected since for large angular momenta there is no direct correspondence between black holes and single-string states. We also develop a random-walk model that describes highly excited strings and accurately reproduces the sizes of rotating strings for all values of angular momentum.