# Horizon Detection and Higher Dimensional Black Rings

## TL;DR

This paper investigates the horizons of five-dimensional rotating and supersymmetric black rings, developing new Cartan invariants that effectively detect horizons and are computationally simpler than traditional scalar polynomial invariants.

## Contribution

It introduces novel Cartan invariants for black ring horizons using algebraic classification and discriminant methods, enhancing horizon detection techniques in higher dimensions.

## Key findings

- Cartan invariants successfully detect black ring horizons
- New algebraic and discriminant methods applied to classify Weyl tensor
- Invariants are computationally simpler than scalar polynomial curvature invariants

## Abstract

In this paper we study the stationary horizons of the rotating black ring and the supersymmetric black ring spacetimes in five dimensions. In the case of the rotating black ring we use Weyl aligned null directions to algebraically classify the Weyl tensor, and utilize an adapted Cartan algorithm in order to produce Cartan invariants. For the supersymmetric black ring we employ the discriminant approach and repeat the adapted Cartan algorithm. For both of these metrics we are able to construct Cartan invariants that detect the horizon alone, and which are easier to compute and analyse that scalar polynomial curvature invariants.