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

TL;DR

This paper introduces curvature invariants that can locally identify the event horizon, ergosurface, and measure the mass and spin of Kerr black holes, aiding in gravitational wave analysis and black hole characterization.

Contribution

It presents new dimensionless invariants derived from curvature that detect horizons, ergosurfaces, and estimate black hole parameters locally.

Findings

Invariants detect the event horizon and ergosurface.

Mass and angular momentum can be extracted from local curvature.

A measure of the Kerrness of spacetime is introduced.

Abstract

We provide an invariant characterization of the physical properties of the Kerr spacetime. We introduce two dimensionless invariants, constructed out of some known curvature invariants, that act as detectors for the event horizon and ergosurface of the Kerr black hole. We also show that the mass and angular momentum can be extracted from local measurements of the curvature invariants, which in the weak field limit could be used to approximate the total angular momentum and mass of a system of merging black holes. Finally, we introduce a dimensionless invariant that gives a local measure of the "Kerrness" of the spacetime.