Gravitational duality, topologically massive gravity and holographic fluids

TL;DR

This paper explores how gravitational self-duality relates boundary data in holography, leading to exact Einstein spaces with nut charge and revealing simplified fluid dynamics with vanishing transport coefficients.

Contribution

It demonstrates the extension of Euclidean self-duality to Lorentzian signatures and its implications for holographic fluids and exact bulk geometries.

Findings

Self-duality relates boundary energy-momentum and Cotton tensors.

Exact Einstein spaces with nut charge are generated.

Infinite transport coefficients vanish in certain fluid states.

Abstract

Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits perfect-fluid-like equilibrium states and the presence of non-trivial vorticity allows to show that infinite number of transport coefficients vanish.