Spinning Strings as Small Black Rings

TL;DR

This paper investigates small black rings in string theory, showing their entropy matches statistical predictions and revealing geometric structures and bounds related to angular momentum.

Contribution

It demonstrates the agreement between supergravity and string theory entropy calculations for spinning black rings and elucidates their near horizon geometry.

Findings

Entropy of black rings matches statistical entropy.

Near horizon geometry determined and related to Regge bound.

Large angular momentum leads to ring-like horizons.

Abstract

Certain supersymmetric elementary string states with spin can be viewed as small black rings whose horizon has the topology of S^1 \times S^{d-3} in a d-dimensional string theory. By analyzing the singular black ring solution in the supergravity approximation, and using various symmetries of the \alpha' corrected effective action we argue that the Bekenstein-Hawking-Wald entropy of the black string solution in the full string theory agrees with the statistical entropy of the same system up to an overall normalization constant. While the normalization constant cannot be determined by the symmetry principles alone, it can be related to a similar normalization constant that appears in the expression for small black holes without angular momentum in one less dimension. Thus agreement between statistical and macroscopic entropy of (d-1)-dimensional non-rotating elementary string states would imply a similar agreement for a d-dimensional elementary string state with spin. Our analysis also determines the structure of the near horizon geometry and provides us with a geometric derivation of the Regge bound. These studies give further evidence that a ring-like horizon is formed when large angular momentum is added to a small black hole.