Superball of Strings

TL;DR

This paper constructs a horizon-free, static bound-state geometry in string theory—the 'Superball of Strings'—that realizes a microcanonical ensemble of highly excited 1/4-BPS strings in a five-dimensional supergravity setting. The solution emerges from averaging the DGHW string-source configurations over the microcanonical sector, yielding a smooth geometry with a Gaussian, random-walk–scaled source size $r_b$ and no horizon, while remaining embedded in string theory under broad parameter regimes. It reproduces a near-core redshift that matches, in appropriate limits, aspects of black-hole-like behavior without a singularity, and it is shown to be trustworthy under weak coupling, small curvature, and large circle size, with T-duality addressing regimes where the y-circle shrinks. The work contrasts this Lorentzian construction with the Euclidean HP and CM&W solutions, finding significant differences in density profiles and entropy counting, and arguing that the Superball is not simply a Lorentzian continuation of CM&W; nevertheless, it provides a concrete, controllable microstate geometry that can be generalized to less supersymmetric settings and rotating configurations, with potential phenomenological implications and a path toward broader understanding of stringy black hole microstates.

Abstract

I solve the equations of the low-energy limit of string theory to obtain a solution corresponding to a microcanonical ensemble of highly-excited superstrings. This ``Superball of Strings'' is a static, spherically symmetric ``fuzzball'' of BPS strings with a size set by a random walk scaling. The solution can be embedded in string theory in a significant part of parameter space. While the solution does not constitute a Lorentzian interpretation for a Euclidean, horizonless solution by Chen, Maldacena, and Witten, a few connections are noted. A singular extremal black hole and the Superball of Strings exist as Supergravity solutions with the same asymptotic boundary conditions; however, I argue that the latter describes generic BPS microstates.