# A gravitating Yang-Mills instanton

## TL;DR

This paper constructs a new, regular, horizonless solution in five-dimensional supergravity using an SU(2) instanton, representing a string-theory object that does not affect black hole entropy, and analyzes its energy distribution.

## Contribution

It introduces a novel asymptotically flat, spherically symmetric solution in 5D supergravity based on the BPST instanton, linking it to a gauge 5-brane in string theory.

## Key findings

- Solution is globally regular and horizonless.
- Energy concentration remains below the hoop conjecture limit.
- Curvature diverges as the instanton scale approaches zero.

## Abstract

We present an asymptotically flat, spherically symmetric, static, globally regular and horizonless solution of SU$(2)$-gauged $\mathcal{N}=1,d=5$ supergravity. The SU$(2)$ gauge field is that of the BPST instanton. We argue that this solution, analogous to the global monopoles found in $d=4$ $\mathcal{N}=2$ and $\mathcal{N}=4$ gauged supergravities, describes the field of a single string-theory object which does not contribute to the entropy of black holes when we add it to them and show that it is, indeed, the dimensional reduction on T$^{5}$ of the gauge 5-brane. We investigate how the energy of the solution is concentrated as a function of the instanton's scale showing that it never violates the hoop conjecture although the curvature grows unboundedly in the zero scale limit.