Identification of black hole horizons using scalar curvature invariants

TL;DR

This paper introduces the concept of geometric horizons defined by scalar curvature invariants, providing a method to detect black hole horizons in various scenarios, including stationary and dynamical cases.

Contribution

It defines geometric horizons via curvature invariants, proves their equivalence to non-expanding horizons, and demonstrates their applicability to spherically symmetric dynamical black holes.

Findings

Scalar invariants vanish on event horizons of stationary black holes.

Geometric horizons coincide with non-expanding horizons.

In dynamical spherically symmetric cases, geometric horizons identify marginally trapped tubes.

Abstract

We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.