Detecting Event Horizons and Stationary Surfaces

Abstract

We have investigated the behavior of three curvature invariants for Schwarzschild, Reissner-Nordstrøm, Kerr, and Kerr-Newman black holes. We have also studied these invariants for a Schwarzschild-de Sitter space-time, the $γ$ metric, and for a 2+1 charged dimensional black hole. The invariants are $I_{1}=R_{αβμν;λ}R^{αβμν;λ}$, $I_{2}=R_{μν;λ} R^{μν;λ}$, and $I_{3}=C_{αβμν;λ}C^{αβμν;λ}$. For all but the Kerr-Newman case these invariants serve as either horizon or stationary surface detectors. The Kerr-Newman case is more complicated. We show that $I_{1}$ vanishs on the horizon in any space-time with a Schwarzschild like metric.