Black hole stability conjecture explained

The black hole stability conjecture is the conjecture that a perturbed Kerr black hole in Minkowski space will settle back down to a stable state. The question developed out of work in 1952 by the French mathematician Yvonne Choquet-Bruhat.^{[1] [2]}

The stability of empty Minkowski space is a result of Klainerman and Christodoulou from 1993.^[3]

A 2016 by Hintz and Vasy paper proved the stability of slowly rotating Kerr black holes in de Sitter space.^[4]

A limited stability result for Kerr black holes in Schwarzschild space-time was published by Klainerman and Szeftel in 2017.^[5]

Culminating in 2022, a series of papers was published by Giorgi, Klainerman and Szeftel which present a proof of the conjecture for slowly rotating Kerr black holes in Minkowski space-time.^{[6] [7] [8]}

See also

• Final state conjecture
• Stability of matter
• Positive energy theorem
• Birkhoff's theorem (relativity)
• Penrose–Hawking singularity theorems
• Hoop conjecture

Notes and References

1. Fourès-Bruhat . Y. . 1952 . Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires . Acta Mathematica . en . 88 . 0 . 141–225 . 10.1007/BF02392131 . 0001-5962. free .
2. Web site: Harnett . Kevin . 8 March 2018 . To Test Einstein’s Equations, Poke a Black Hole . Quanta Magazine.
3. Book: Christodoulou, Demetrios . The global nonlinear stability of the Minkowski space . Klainerman . Sergiu . 1993 . Princeton university press . 978-0-691-08777-1 . Princeton mathematical series . Princeton.
4. Hintz . Peter . Vasy . András . 2018 . The global non-linear stability of the Kerr-de Sitter family of black holes . Acta Mathematica . 220 . 1 . 1–206 . 10.4310/acta.2018.v220.n1.a1. 1606.04014 . 119281798 .
5. Klainerman . Sergiu . Szeftel . Jeremie . 2018-12-20 . Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations . gr-qc . 1711.07597 .
6. Web site: Nadis . Steve . 2022-08-04 . Black Holes Finally Proven Mathematically Stable . 2022-08-05 . Quanta Magazine . en.
7. Klainerman . Sergiu . Szeftel . Jeremie . 2021-04-23 . Kerr stability for small angular momentum . math.AP . 2104.11857 .
8. Giorgi . Elena . Klainerman . Sergiu . Szeftel . Jeremie . 2022-05-30 . Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes . math.AP . en . 2205.14808.