Rotating black holes and Coriolis effect

Chia-Jui Chou,Pei-Hung Yuan,Yi Yang,Xiaoning Wu

doi:10.1016/j.physletb.2016.08.018

Chia-Jui Chou, Pei-Hung Yuan + Show 2 more

Open Access

https://doi.org/10.1016/j.physletb.2016.08.018

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Abstract

Abstract In this work, we consider the fluid/gravity correspondence for general rotating black holes. By using the suitable boundary condition in near horizon limit, we study the correspondence between gravitational perturbation and fluid equation. We find that the dual fluid equation for rotating black holes contains a Coriolis force term, which is closely related to the angular velocity of the black hole horizon. This can be seen as a dual effect for the frame-dragging effect of rotating black hole under the holographic picture.

Highlights

It is well-known that gauge/gravity correspondence is a great breakthrough on theoretical physics
In this paper we studied the fluid/gravity correspondence for a general rotating black hole
We considered a rotating black hole with an isolated horizon, which is more general than an usual stationary horizon since only the geometry inside the horizon is required to be stationary in this case

Summary

Introduction

It is well-known that gauge/gravity correspondence is a great breakthrough on theoretical physics. In 2011, Strominger and his colleagues proposed a new idea to realize the correspondence [16] They found that, by imposing a carefully chosen boundary condition, the perturbed Einstein equation exactly reduces to the Navier–Stokes equation in one lower dimension. This method is much simpler than the original one and can be generalized to the cases of more general black holes. We study the fluid/gravity correspondence for rotating black holes using Strominger’s boundary condition method.

Asymptotic behavior of metric near horizon

Brown–York tensor of the boundary near horizon

Petrov-like boundary condition and gravitational perturbation

The dual Navier–Stokes equation

Conclusion