Research collection / 01

The uniqueness of smooth stationary black holes

Huang, Yishen, Li, Jiongyue, Li, Junbin, Zhu, Xi-Ping

The article studies uniqueness of smooth stationary vacuum black holes without assuming analyticity. This collection presents a conditional theorem with explicit exterior-section, end-access, and Kerr-identification hypotheses.

The proof uses a Harrison transformation and area–charge estimates. In the limiting geometry, the bifurcation sphere has area radius one and constant electric and magnetic flux densities when the original ADM mass is normalized to one.

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Research & notes

28 entries

Prerequisites

Article items and immediate prerequisites

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Level 0

6 pages

Article items · 01 — Cauchy-Schwarz inequality for L²28 items
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Article items · 02 — The Lie derivative of a tensor field28 items
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Article items · 03 — The fundamental theorem of calculus and integration by parts28 items
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Article items · 04 — In a Hausdorff space a point and a disjoint compact set, and two disjoint compact sets, have disjoint open neighbourhoods; hence every compact subset is closed, and in a compact Hausdorff space the compact subsets are exactly the closed ones28 items
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Article items · 05 — The Lie derivative of a vector field equals the Lie bracket28 items
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Article items · 06 — Null normal pairs and screen geometry28 items
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.

Level 1

1 page

Article items · 07 — Asymptotically flat spacelike end and derivative decay29 items
Presents 29 items from the article and its immediate prerequisites, covering dependency level 0.

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1 page

Article items · 08 — Periods and primitives on a spherical exterior28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 0–1.

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1 page

Article items · 09 — Compact causal diamonds close the selected-generator endpoint domain28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 1–2.

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1 page

Article items · 10 — Regular non-degenerate stationary vacuum spacetime28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency level 2.

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1 page

Article items · 11 — ADM section time and causal spatial speed28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 2–3.

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1 page

Article items · 12 — A smooth spacelike reference section is a bounded rapidity graph28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 3–4.

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1 page

Article items · 13 — Weighted cutoff maximum gives a uniform normal angle29 items
Presents 29 items from the article and its immediate prerequisites, covering dependency levels 4–5.

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1 page

Article items · 14 — Geometric data for the analytic multiple-horizon comparison28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency level 5.

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1 page

Article items · 15 — Hawking horizon generator and analytic global rigidity28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 5–6.

Level 10

1 page

Article items · 16 — Non-rotating staticity and Schwarzschild uniqueness28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 6–8.

Level 11

1 page

Article items · 17 — The zero-parameter spatial cylinder and its limiting area28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 8–10.

Level 12

1 page

Article items · 18 — Asymptotically flat positive-q ends and cylindrical limit28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 10–19.

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Article items · 19 — Cutoff maximum principle and uniform collar regularity29 items
Presents 29 items from the article and its immediate prerequisites, covering dependency levels 19–40.

Assessed 15 Nov 2026, 05:45 UTC
Prerequisite omissions and potential defects
Original-article findings for The uniqueness of smooth stationary black holes.

Assessed 15 Nov 2026, 05:45 UTC
Open questions and potential solutions
Insights, fruitful questions and potential solutions arising from The uniqueness of smooth stationary black holes.

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The uniqueness of smooth stationary black holes

Research & notes

Prerequisites

Harrison fields, horizons and uniqueness inputs

Maximal slices, causal cuts and stability

Stationary geometry and analytic data

Supporting prerequisites · 01 — Gauss lemma

Supporting prerequisites · 02 — Local compactness of full weighted Hölder inputs

Supporting prerequisites · 03 — Komar flux equals the original stationary mass coefficient

Article items and immediate prerequisites

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Prerequisite omissions and potential defects

Open questions and potential solutions