Blackfolds, Plane Waves and Minimal Surfaces

TL;DR

This paper explores new black hole horizon geometries using the blackfold approach, revealing novel configurations like black helicoids and catenoids in various space-times, and connecting ultraspinning black holes with minimal surface limits.

Contribution

It introduces new black hole horizon geometries based on minimal surfaces in different space-times, expanding the landscape of possible black hole solutions.

Findings

Discovery of black helicoids and catenoids as horizon geometries.

Connection between ultraspinning black holes and minimal surface limits.

Construction of static horizons in de Sitter space using minimal surfaces in spheres.

Abstract

Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.