Fermionic wigs for AdS-Schwarzschild black holes

Abstract

We provide the metric, the gravitino fields and the gauge fields to all orders in the fermionic zero modes for D = 5 and D = 4, N = 2 gauged supergravity solutions starting from non-extremal AdS-Schwarzschild black holes. We compute the Brown-York stress-energy tensor on the boundary of AdS 5/AdS4 spaces and we discuss some implications of the fermionic corrections to perfect fluid interpretation of the boundary theory. The complete non-linear solution, which we denote as fermionic wig, is achieved by acting with supersymmetry transformations upon the supergravity fields and that expansion naturally truncates at some order in the fermionic zero modes

Fermionic corrections to fluid dynamics from BTZ black hole

“…Having added fermionic fields to our scheme, the Navier-Stokes equations are now dual to the equations of motion derived from the N = 2, D = 3 AdS−supergravity action (2.2). 10 Once the fermionic bilinears are taken into account, imposing equations of motion (2.6) and taking the large r limit, we find:…”

“…In a previous paper [8], we computed the full supermultiplet of the BTZ black hole by performing a finite susy transformation. Notice that only by finite susy transformations, we are able to compute the complete orbit (wig) starting from the black hole solutions [9,10]. That susy transformation truncates at the forth order.…”

No fermionic wigs for BPS attractors in 5 dimensions

“…e.g. [14,6]); schematically denoting all wigged fields as Φ and the original bosonic configuration by Φ, the following expansion holds:…”

Fermionic wigs for BTZ black holes

“…In [1] we constructed the complete solution (named "wig" to recall that all fermionic hairs are resummed into a complete non-linear solution) starting from non-extremal black holes for N = 2, D = 5 and D = 4 supergravity. The construction presented in that work was based on a Mathematica R package used to "integrate" the fermionic zero modes of the solution into the metric and the other fields.…”

“…Our motivations stem from the fluid/gravity correspondence discovered in [10,11] and extended in [1] to fermionic degrees of freedom. Starting from a solution of a gravity/supergravity theory on AdS background such as black hole or black-brane solution, one acts with certain isometries transformations whose parameters depend on AdS-boundary coordinates.…”