GRG Editor's Choice: Cartan invariants and event horizon detection

© SpringerBrooks, D., Chavy-Waddy, P.C., Coley, A.A. et al., Cartan invariants and event horizon detection, Gen Relativ Gravit (2018) 50: 37.

Editor's Choice (Research Article)

First Online: 12 March 2018

"This well-written paper contains important new results: The authors show by giving concrete examples that the Cartan invariants are more useful than the traditional scalar polynomial invariants in finding location of event horizons. As particular examples they consider in 4 dimensions the Kerr-Newman-NUT-(Anti)de Sitter metric and in 5 dimensions the Reissner-Nordström-(Anti)deSitter metric and the Kerr-NUT-(Anti)deSitter metric. It turns out that for complicated metrics it is much easier to calculate the Cartan invariants than the scalar polynomial invariants. This could help to find event horizons in numerical models describing collapsing stars and the process of merging of two or more black holes."


We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.

The authors: 

Dario Brooks, Paul-Christopher Chavy-Waddy, Alan A. Coley, Adam Forget, and Daniele Gregoris are researchers at Dalhousie University in Halifax, Nova Scotia, Canada. Malcolm A. H. MacCallum is Emeritus Professor of Applied Mathematics at Queen Mary University of London. David D. McNutt is working at the University of Stavanger, Norway.

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.