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Related Experiment Video

Updated: Jun 8, 2026

Quantifying Intermembrane Distances with Serial Image Dilations

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Geometric invariant measuring the deviation from Kerr data.

Thomas Bäckdahl¹, Juan A Valiente Kroon

¹School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom. t.backdahl@qmul.ac.uk

Physical Review Letters

|September 28, 2010

Summary

A new geometric invariant identifies slices of the Kerr black hole spacetime. This tool measures deviations from Kerr black hole behavior in general relativity data, utilizing approximate Killing spinors.

Related Experiment Videos

Last Updated: Jun 8, 2026

Quantifying Intermembrane Distances with Serial Image Dilations

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Area of Science:

General Relativity
Mathematical Physics
Black Hole Physics

Background:

The Kerr black hole spacetime is a fundamental solution to Einstein's field equations.
Characterizing general solutions and their deviations from known solutions like Kerr is crucial.

Purpose of the Study:

To construct a geometrical invariant for asymptotically Euclidean vacuum Einstein data.
To provide a method for distinguishing Kerr black hole spacetimes from other solutions.

Main Methods:

Introduction of approximate Killing spinors.
Development of a geometrical invariant based on these spinors.
Analysis of the invariant's properties for regular asymptotically Euclidean data.

Main Results:

A novel geometrical invariant is successfully constructed.
The invariant is shown to vanish if and only if the data represent a slice of the Kerr black hole spacetime.
The invariant quantifies non-Kerr-like behavior in generic data.

Conclusions:

The constructed invariant serves as a definitive measure for Kerr black hole spacetimes.
Approximate Killing spinors are a key tool for analyzing vacuum Einstein field equations.
This work offers a new perspective on classifying black hole solutions in general relativity.