Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes

TL;DR

This paper introduces a new method using local scalar polynomial curvature invariants that vanish on stationary black hole horizons, providing a diagnostic tool for black hole detection.

Contribution

It constructs a universal set of local invariants based on wedge products of gradients, applicable to any stationary black hole, extending previous specific examples.

Findings

Invariants vanish precisely on black hole horizons

Applicable to all stationary black holes

Provides a coordinate-independent diagnostic tool

Abstract

Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime.