Fermionic Corrections to Fluid Dynamics from BTZ Black Hole

TL;DR

This paper explores fermionic corrections to fluid dynamics derived from the BTZ black hole, revealing how supersymmetry transformations influence the fluid's properties and entropy in the context of supergravity and holography.

Contribution

It reconstructs the fermionic orbit of the BTZ black hole and derives modified fluid dynamics equations incorporating fermionic effects.

Findings

Derived linearized Navier-Stokes equations with fermionic corrections

Computed boundary energy-momentum tensor showing a modified fluid velocity

Obtained a new expression for black hole entropy involving fermionic bilinears

Abstract

We reconstruct the complete fermionic orbit of the non-extremal BTZ black hole by acting with finite supersymmetry transformations. The solution satisfies the exact supergravity equations of motion to all orders in the fermonic expansion and the final result is given in terms of fermionic bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes equations and a set of new differential equations from Rarita-Schwinger equation. We compute the boundary energy-momentum tensor and we interpret the result as a perfect fluid with a modified definition of fluid velocity. Finally, we derive the modified expression for the entropy of the black hole in terms of the fermionic bilinears.