New Geometries for Black Hole Horizons

TL;DR

This paper develops new effective theories for higher-dimensional black holes by integrating out spatial sections, leading to novel horizon geometries like black rings and helicoidal branes, and extends the blackfold approach.

Contribution

It generalizes the blackfold method for higher-dimensional black holes and introduces new effective theories and horizon geometries using Euclidean minimal surfaces.

Findings

Derived new hydrodynamic and elastic transport coefficients.

Constructed novel black hole horizon geometries including black rings and helicoidal structures.

Extended the blackfold approach to include complex geometries in higher dimensions.

Abstract

We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal $p$-branes as well as helicoidal black rings and helicoidal black tori in $D\ge6$.