Quantum hair and the string-black hole correspondence

TL;DR

This paper investigates how a massless string interacting with a stringhole can reveal microstate information, challenging the assumption that quantum hair is exponentially suppressed, with implications for the black hole information paradox.

Contribution

It demonstrates that the scattering matrix is sensitive to stringhole microstates, providing evidence against the exponential suppression of quantum hair.

Findings

The S-matrix depends on the stringhole's quadrupole moment.

Quantum hair is not exponentially suppressed as previously assumed.

Implications for resolving the black hole information paradox.

Abstract

We consider a thought experiment in which an energetic massless string probes a "stringhole" (a heavy string lying on the correspondence curve between strings and black holes) at large enough impact parameter for the regime to be under theoretical control. The corresponding, explicitly unitary, $S$-matrix turns out to be perturbatively sensitive to the microstate of the stringhole: in particular, at leading order in $l_s/b$, it depends on a projection of the stringhole's Lorentz-contracted quadrupole moment. The string-black hole correspondence is therefore violated if one assumes quantum hair to be exponentially suppressed as a function of black-hole entropy. Implications for the information paradox are briefly discussed.