Fluids and vortex from constrained fluctuations around C-metric black hole

TL;DR

This paper explores how perturbations around a C-metric black hole can be described by fluid dynamics equations, revealing vortex behavior and viscosity properties influenced by black hole acceleration.

Contribution

It introduces a novel holographic initial data formulation for C-metric black holes and derives fluid equations governing perturbations in this setting.

Findings

Fluctuation modes obey Navier-Stokes and continuity equations.

The fluid exhibits vortex behavior.

Viscosity to entropy ratio depends on black hole acceleration.

Abstract

By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic initial data is a double consisting of the induced metric and the Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by perturbing the initial data that generates the background spacetime, it is shown that, in an appropriate limit, the fluctuation modes are governed by the continuity equation and the compressible Navier-Stokes equation which describe the momentum transport in non-relativistic viscous fluid on a flat Newtonian space. It turns out that the flat space fluid behaves as a pure vortex and the viscosity to entropy ratio is subjected to the black hole acceleration.