Numerical implementations of holographic duality via the fluid/gravity correspondence

Abstract

The fluid/gravity correspondence describes an map from relativistic fluid dynamics to general relativity in an anti de Sitter (AdS) background in one more dimension. This is a specific example of a more general principle known as holographic duality, in which a quantum field theory (QFT) is dual to a gravitational theory with the QFT defined on the boundary. Since we can regard hydrodynamics as a low-energy description of many QFTs, the fluid/gravity correspondence lets us probe holographic duality for QFTs at low energy. In this thesis, we will discuss holographic duality, hydrodynamic theory and turbulence, numerical implementations of hydrodynamics, black branes in AdS, the fluid/gravity correspondence, and numerically testing the fluid/gravity correspondence.