Characteristic gluing to extremal Kerr horizons and the third law of black hole thermodynamics in vacuum
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Stefan Czimek · arXiv: 2610.35836v1 · Summary page
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An extremal black hole, reached through vacuum
Can a black hole evolve into an extremal state, where its rotation reaches the limiting value allowed by its mass? A new preprint constructs a counterexample in vacuum to the third law of black-hole thermodynamics. The authors build initial conditions whose subsequent spacetime contains an exactly Schwarzschild apparent horizon and, later, an exactly extremal Kerr event horizon. The distinction between apparent and event horizons matters: the construction connects different kinds of horizon, rather than simply tracking a single locally defined surface.
The mathematical engine is a gluing theorem for Einstein’s vacuum equations. Rotating pulses of gravitational radiation raise the angular momentum, while a long intervening region suppresses unwanted incoming data. A final matching argument handles the extremal horizon exactly, including curvature information transverse to it. The result shows that vacuum general relativity permits a route that a familiar thermodynamic prohibition would appear to exclude; it is an existence proof, not a prediction that astrophysical black holes ordinarily follow this route.
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