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 $\gamma$ metric, and for a 2+1 charged dimensional black hole. The invariants are $I_1=R_{\alpha \beta \mu \nu ;\lambda }{R}^{\alpha \beta \mu \nu ;\lambda }$, $I_2=R_{\mu \nu ;\lambda }{R}^{\mu \nu ;\lambda }$, and $I_3=C_{\alpha \beta \mu \nu ;\lambda }{C}^{\alpha \beta \mu \nu ;\lambda }$. 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.

arXiv comment23 pages, 13 figures

Cited by in corpus (1)

• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants