A Note on D1-D5-J System and 5D Small Black Ring

TL;DR

This paper explores the microscopic and macroscopic properties of the 5D small black ring, relating it to a 4D black hole via duality, and provides evidence for horizon formation due to stringy corrections, aligning microscopic and macroscopic entropies.

Contribution

It establishes a connection between 5D small black rings and 4D black holes, showing horizon formation and matching entropies through duality and stringy corrections.

Findings

The 4D-5D connection holds for small black objects.

Stringy R^2 corrections induce horizon formation.

Microscopic entropy matches macroscopic calculations.

Abstract

The ``small'' black ring in 5D obtained by giving angular momentum to the D1-D5 system compactified on S^1 x K3 is a very interesting object in the sense that it does not have an event horizon in the supergravity limit whereas it microscopically has a finite entropy. The microscopic origin of this small black ring can be analyzed in detail since it is constructed by adding angular momentum to the well-studied D1-D5 system. On the other hand, its macroscopic, geometrical picture is difficult to study directly. In this note, by duality transformations and the 4D-5D connection, we relate this 5D small black ring to a 4D small non-rotating black hole, where the latter is known to develop a non-vanishing horizon due to stringy R^2 corrections to the supergravity action. This gives an indirect evidence that a non-vanishing horizon is formed for the 5D small black ring. We also show that the entropy of the 4D small black hole agrees with the microscopic entropy of the 5D small black ring, which supports that the 4D-5D connection is indeed valid even for small black objects.