Kerr black-hole spin bound

Classical Kerr spacetime has an event horizon only at or below unit dimensionless spin.

Specification version 1Published 1963-09-011 evidence records

About this problem

The question, scope, and sources behind this Registry record.

Formal question

Require real Kerr horizon radii r_± for an asymptotically flat uncharged stationary black hole.

Scope & constraints

charge: 0
object: Kerr black hole
gravity: classical general relativity
stationary: true
asymptotics: flat

Primary sources

Gravitational field of a spinning mass as an example of algebraically special metrics — Kerr black-hole spin bound Kerr metric and horizon condition

What we know

Current frontiers derived from accepted Claims.

KNOWN LOWER BOUNDKNOWN UPPER BOUND

Unknown

OPEN FRONTIER

|a_*| = |Jc/(GM^2)| <= 1

Lower boundGap: UnknownUpper bound

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-ASTRO-003505<= |a_*| = |Jc/(GM^2)| <= 1UPPER BOUNDThe cited theorem establishes |a_*| = |Jc/(GM^2)| <= 1 under the recorded model.Source: Gravitational field of a spinning mass as an example of algebraically special metrics — Kerr black-hole spin bound ↗

PROVEN

Timeline

The frontier as it changed over time.

How this frontier is derived

Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.

—No breakthrough events recorded yetEvents appear here when an accepted Claim tightens a bound or closes the frontier.