Horizon Detection and Higher Dimensional Black Rings

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.