Fermionic Wigs for BTZ Black Holes

TL;DR

This paper constructs the complete fermionic extension (wig) of the BTZ black hole in supergravity, including all fermionic zero modes, and analyzes the back-reaction on the metric and physical charges.

Contribution

It introduces a gauge completion method to derive the full non-linear fermionic solution for BTZ black holes, including explicit calculations of back-reaction and conserved charges.

Findings

Fermionic wig truncates at finite order due to anticommutativity.

Explicit analytical form of the fermionic solution is provided.

Corrections to mass and angular momentum are computed.

Abstract

We compute the wig for the BTZ black hole, namely the complete non-linear solution of supergravity equations with all fermionic zero modes. We use a "gauge completion" method starting from AdS_3 Killing spinors to generate the gravitinos fields associated to the BH and we compute the back-reaction on the metric. Due to the anticommutative properties of the fermionic hairs the resummation of these effects truncates at some order. We illustrate the technique proposed in a precedent paper in a very explicit and analytical form. We also compute the mass, the angular momentum and other charges with their corrections.