@misc{HHV2025,
  author        = {H{\"a}fner, Dietrich and Hintz, Peter and Vasy, Andr{\'a}s},
  title         = {Linear stability of {Kerr} black holes in the full subextremal range},
  year          = {2025},
  eprint        = {2506.21183},
  howpublished  = {arXiv:2506.21183v1},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  doi           = {10.48550/arXiv.2506.21183},
  url           = {https://arxiv.org/abs/2506.21183v1},
  note          = {Version 1, 26 June 2025}
}

@article{Dyatlov2016,
  author        = {Dyatlov, Semyon},
  title         = {Spectral gaps for normally hyperbolic trapping},
  journal       = {Annales de l'Institut Fourier},
  volume        = {66},
  number        = {1},
  year          = {2016},
  pages         = {55--82},
  doi           = {10.5802/aif.3005},
  eprint        = {1403.6401v3},
  archivePrefix = {arXiv},
  primaryClass  = {math.AP},
  url           = {https://aif.centre-mersenne.org/articles/10.5802/aif.3005/}
}

@article{Hintz2017,
  author        = {Hintz, Peter},
  title         = {Resonance expansions for tensor-valued waves on asymptotically {Kerr--de Sitter} spaces},
  journal       = {Journal of Spectral Theory},
  volume        = {7},
  number        = {2},
  year          = {2017},
  pages         = {519--557},
  doi           = {10.4171/JST/171},
  eprint        = {1502.03183v2},
  archivePrefix = {arXiv},
  primaryClass  = {math.AP},
  url           = {https://ems.press/journals/jst/articles/14842}
}

@article{DafermosLuk2017,
  author        = {Dafermos, Mihalis and Luk, Jonathan},
  title         = {The interior of dynamical vacuum black holes {I}: The {$C^0$}-stability of the {Kerr Cauchy} horizon},
  journal       = {Annals of Mathematics},
  series        = {2},
  volume        = {202},
  number        = {2},
  year          = {2025},
  pages         = {309--630},
  doi           = {10.4007/annals.2025.202.2.1},
  eprint        = {1710.01722v1},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  url           = {https://annals.math.princeton.edu/2025/202-2/p01},
  note          = {Preprint first posted in 2017}
}

@article{ChoquetBruhat1952,
  author        = {Four{\`e}s-Bruhat, Yvonne},
  title         = {Th{\'e}or{\`e}me d'existence pour certains syst{\`e}mes d'{\'e}quations aux d{\'e}riv{\'e}es partielles non lin{\'e}aires},
  journal       = {Acta Mathematica},
  volume        = {88},
  year          = {1952},
  pages         = {141--225},
  doi           = {10.1007/BF02392131},
  url           = {https://link.springer.com/article/10.1007/BF02392131}
}

@article{ChoquetBruhatGeroch1969,
  author        = {Choquet-Bruhat, Yvonne and Geroch, Robert},
  title         = {Global aspects of the {Cauchy} problem in general relativity},
  journal       = {Communications in Mathematical Physics},
  volume        = {14},
  year          = {1969},
  pages         = {329--335},
  doi           = {10.1007/BF01645389},
  url           = {https://link.springer.com/article/10.1007/BF01645389}
}

@misc{Hintz2026,
  author        = {Hintz, Peter},
  title         = {Nonlinear stability of subextremal {Kerr} black holes},
  year          = {2026},
  eprint        = {2606.28253},
  howpublished  = {arXiv:2606.28253v2},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  doi           = {10.48550/arXiv.2606.28253},
  url           = {https://arxiv.org/abs/2606.28253v2},
  note          = {Version 2, 3 August 2026; first posted 26 June 2026}
}

@misc{Gurriaran2026,
  author        = {Gurriaran, Sebastian},
  title         = {Non-linear instability of the {Kerr Cauchy} horizon near {$i_+$}},
  year          = {2026},
  eprint        = {2603.17911},
  howpublished  = {arXiv:2603.17911v2},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  doi           = {10.48550/arXiv.2603.17911},
  url           = {https://arxiv.org/abs/2603.17911v2},
  note          = {Version 2, 23 March 2026}
}

@article{Penrose1969,
  author        = {Penrose, Roger},
  title         = {Gravitational collapse: The role of general relativity},
  journal       = {General Relativity and Gravitation},
  volume        = {34},
  number        = {7},
  year          = {2002},
  pages         = {1141--1165},
  doi           = {10.1023/A:1016578408204},
  url           = {https://doi.org/10.1023/A:1016578408204},
  note          = {Reprint of the 1969 article}
}

@misc{LukSbierski2026,
  author        = {Luk, Jonathan and Sbierski, Jan},
  title         = {The formation of a weak null singularity in the interior of generic rotating black holes},
  year          = {2026},
  eprint        = {2604.04877},
  howpublished  = {arXiv:2604.04877v1},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  doi           = {10.48550/arXiv.2604.04877},
  url           = {https://arxiv.org/abs/2604.04877v1},
  note          = {Version 1, 6 April 2026}
}

@article{LindbladRodnianski2003,
 author={Lindblad, Hans and Rodnianski, Igor},
 title={The weak null condition for {Einstein}'s equations},
 journal={Comptes Rendus. Math{\'e}matique},
 volume={336}, number={11}, pages={901--906}, year={2003},
 doi={10.1016/S1631-073X(03)00231-0},
 url={https://www.numdam.org/articles/10.1016/S1631-073X(03)00231-0/}
}

@article{LindbladRodnianski2010,
 author={Lindblad, Hans and Rodnianski, Igor},
 title={The global stability of {Minkowski} space-time in harmonic gauge},
 journal={Annals of Mathematics}, volume={171}, number={3},
 pages={1401--1477}, year={2010},
 doi={10.4007/annals.2010.171.1401},
 eprint={math/0411109}, archivePrefix={arXiv},
 url={https://annals.math.princeton.edu/2010/171-3/p01}
}

@article{DafermosRodnianski2009,
 author={Dafermos, Mihalis and Rodnianski, Igor},
 title={The red-shift effect and radiation decay on black hole spacetimes},
 journal={Communications on Pure and Applied Mathematics},
 volume={62}, number={7}, pages={859--919}, year={2009},
 doi={10.1002/cpa.20281},
 eprint={gr-qc/0512119}, archivePrefix={arXiv},
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}

@inproceedings{DafermosRodnianski2010,
 author={Dafermos, Mihalis and Rodnianski, Igor},
 title={A new physical-space approach to decay for the wave equation with applications to black hole spacetimes},
 booktitle={XVIth International Congress on Mathematical Physics},
 editor={Exner, Pavel}, publisher={World Scientific},
 pages={421--433}, year={2010},
 doi={10.1142/9789814304634_0032},
 eprint={0910.4957}, archivePrefix={arXiv},
 url={https://arxiv.org/abs/0910.4957}
}

@article{DafermosRodnianskiShlapentokhRothman2016,
 author={Dafermos, Mihalis and Rodnianski, Igor and Shlapentokh-Rothman, Yakov},
 title={Decay for solutions of the wave equation on {Kerr} exterior spacetimes {III}: The full subextremal case {$|a|<M$}},
 journal={Annals of Mathematics}, volume={183}, number={3},
 pages={787--913}, year={2016},
 doi={10.4007/annals.2016.183.3.2},
 eprint={1402.7034}, archivePrefix={arXiv},
 url={https://annals.math.princeton.edu/2016/183-3/p02}
}

@article{DafermosRodnianskiShlapentokhRothman2018,
 author={Dafermos, Mihalis and Rodnianski, Igor and Shlapentokh-Rothman, Yakov},
 title={A scattering theory for the wave equation on {Kerr} black hole exteriors},
 journal={Annales Scientifiques de l'{\'E}cole Normale Sup{\'e}rieure},
 series={4}, volume={51}, number={2}, pages={371--486}, year={2018},
 doi={10.24033/asens.2358},
 eprint={1412.8379}, archivePrefix={arXiv},
 url={https://arxiv.org/abs/1412.8379}
}

@article{DafermosHolzegelRodnianski2019,
 author={Dafermos, Mihalis and Holzegel, Gustav and Rodnianski, Igor},
 title={Boundedness and decay for the {Teukolsky} equation on {Kerr} spacetimes {I}: The case {$|a|\ll M$}},
 journal={Annals of PDE}, volume={5}, number={1},
 pages={2}, year={2019}, note={Article 2},
 doi={10.1007/s40818-018-0058-8},
 eprint={1711.07944}, archivePrefix={arXiv},
 url={https://arxiv.org/abs/1711.07944}
}

@misc{ShlapentokhRothmanTeixeiraDaCosta2023,
 author={Shlapentokh-Rothman, Yakov and Teixeira da Costa, Rita},
 title={Boundedness and decay for the {Teukolsky} equation on {Kerr} in the full subextremal range {$|a|<M$}: Physical space analysis},
 year={2023}, eprint={2302.08916}, archivePrefix={arXiv},
 primaryClass={gr-qc},
 doi={10.48550/arXiv.2302.08916},
 url={https://arxiv.org/abs/2302.08916v2},
 note={Version 2, February 21, 2023}
}

@article{HafnerHintzVasy2021,
 author={H{\"a}fner, Dietrich and Hintz, Peter and Vasy, Andr{\'a}s},
 title={Linear stability of slowly rotating {Kerr} black holes},
 journal={Inventiones Mathematicae}, volume={223},
 pages={1227--1406}, year={2021},
 doi={10.1007/s00222-020-01002-4},
 eprint={1906.00860}, archivePrefix={arXiv},
 url={https://arxiv.org/abs/1906.00860}
}

@article{AnderssonHafnerWhiting2026,
 author={Andersson, Lars and H{\"a}fner, Dietrich and Whiting, Bernard F.},
 title={Mode analysis for the linearized {Einstein} equations on the {Kerr} metric: The large {$\mathfrak a$} case},
 journal={Journal of the European Mathematical Society},
 volume={28}, number={9}, pages={3919--3981}, year={2026},
 doi={10.4171/JEMS/1544},
 eprint={2207.12952}, archivePrefix={arXiv},
 url={https://ems.press/journals/jems/articles/14298199}
}

@article{TeixeiraDaCosta2020,
 author={Teixeira da Costa, Rita},
 title={Mode stability for the {Teukolsky} equation on extremal and subextremal {Kerr} spacetimes},
 journal={Communications in Mathematical Physics},
 volume={378}, number={1}, pages={705--781}, year={2020},
 doi={10.1007/s00220-020-03796-z},
 eprint={1910.02854}, archivePrefix={arXiv},
 url={https://link.springer.com/article/10.1007/s00220-020-03796-z}
}

@misc{DafermosHolzegelRodnianskiTaylor2024,
 author={Dafermos, Mihalis and Holzegel, Gustav and Rodnianski, Igor and Taylor, Martin},
 title={Quasilinear wave equations on {Kerr} black holes in the full subextremal range {$|a|<M$}},
 year={2024}, eprint={2410.03639}, archivePrefix={arXiv},
 primaryClass={gr-qc}, doi={10.48550/arXiv.2410.03639},
 url={https://arxiv.org/abs/2410.03639}
}

@misc{KlainermanSzeftel2021,
 author={Klainerman, Sergiu and Szeftel, J{\'e}r{\'e}mie},
 title={{Kerr} stability for small angular momentum},
 year={2021}, eprint={2104.11857}, archivePrefix={arXiv},
 primaryClass={math.AP}, doi={10.48550/arXiv.2104.11857},
 url={https://arxiv.org/abs/2104.11857}
}

@misc{GiorgiKlainermanSzeftel2022,
 author={Giorgi, Elena and Klainerman, Sergiu and Szeftel, J{\'e}r{\'e}mie},
 title={Wave equations estimates and the nonlinear stability of slowly rotating {Kerr} black holes},
 year={2022}, eprint={2205.14808}, archivePrefix={arXiv},
 primaryClass={math.AP}, doi={10.48550/arXiv.2205.14808},
 url={https://arxiv.org/abs/2205.14808}
}


@article{Corvino2000,
  author = {Corvino, Justin},
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@article{CorvinoSchoen2006,
  author = {Corvino, Justin and Schoen, Richard M.},
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  eprint = {gr-qc/0301071}, archivePrefix = {arXiv}
}

@book{ChruscielDelay2003,
  author = {Chru{\'s}ciel, Piotr T. and Delay, Erwann},
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  series = {M{\'e}moires de la Soci{\'e}t{\'e} Math{\'e}matique de France, Nouvelle s{\'e}rie},
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@article{CarlottoSchoen2016,
  author = {Carlotto, Alessandro and Schoen, Richard},
  title = {Localizing Solutions of the {Einstein} Constraint Equations},
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  pages = {559--615}, year = {2016}, doi = {10.1007/s00222-015-0642-4},
  url = {https://doi.org/10.1007/s00222-015-0642-4},
  eprint = {1407.4766}, archivePrefix = {arXiv}
}

@incollection{Bogovskii1980,
  author = {Bogovski{\u\i}, M. E.},
  title = {Solutions of Some Problems of Vector Analysis Associated with the Operators div and grad},
  booktitle = {Theory of Cubature Formulas and the Application of Functional Analysis to Problems of Mathematical Physics},
  series = {Trudy Seminara S. L. Soboleva}, number = {1},
  publisher = {Akademiya Nauk SSSR, Sibirskoe Otdelenie, Institut Matematiki},
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}

@article{CostabelMcIntosh2010,
  author = {Costabel, Martin and McIntosh, Alan},
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  url = {https://doi.org/10.1007/s00209-009-0517-8},
  eprint = {0808.2614}, archivePrefix = {arXiv}
}

@incollection{Ralston1982,
  author = {Ralston, James},
  title = {{Gaussian} Beams and the Propagation of Singularities},
  editor = {Littman, Walter}, booktitle = {Studies in Partial Differential Equations},
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}

@article{Tanushev2008,
  author = {Tanushev, Nicolay M.},
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@article{LiuRunborgTanushev2013,
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@misc{AretakisCzimekRodnianski2021,
  author = {Aretakis, Stefanos and Czimek, Stefan and Rodnianski, Igor},
  title = {The Characteristic Gluing Problem for the {Einstein} Vacuum Equations. Linear and Non-linear Analysis},
  year = {2021}, eprint = {2107.02449}, archivePrefix = {arXiv}, primaryClass = {gr-qc},
  url = {https://arxiv.org/abs/2107.02449v1}, note = {Version 1, July 6, 2021}
}

@misc{CzimekRodnianski2022,
  author = {Czimek, Stefan and Rodnianski, Igor},
  title = {Obstruction-free Gluing for the {Einstein} Equations},
  year = {2022}, eprint = {2210.09663}, archivePrefix = {arXiv}, primaryClass = {gr-qc},
  url = {https://arxiv.org/abs/2210.09663v1}, note = {Version 1, October 18, 2022}
}


@article{AmbroseSinger1953,
 author={Ambrose, Warren and Singer, Isadore M.},
 title={A theorem on holonomy},
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}


@misc{CameronSbierski2025Extensions,
 author={Cameron, Peter and Sbierski, Jan},
 title={On the uniqueness of continuous spacetime extensions in {$1+1$} dimensions with applications to weak null singularities},
 year={2025}, eprint={2511.13422}, archivePrefix={arXiv},
 primaryClass={gr-qc}, url={https://arxiv.org/abs/2511.13422}
}


@misc{CameronSbierski2026Ls,
 author={Cameron, Peter and Sbierski, Jan},
 title={Spherically symmetric inextendibility of weak null singularities with {Christoffel} symbols in {$L^s_{\mathrm{loc}}$}},
 year={2026}, eprint={2609.05167v1}, archivePrefix={arXiv},
 primaryClass={gr-qc}, url={https://arxiv.org/abs/2609.05167v1},
 note={Submitted September 4, 2026}
}


@article{Carter1968,
  author={Carter, Brandon},
  title={Global structure of the {Kerr} family of gravitational fields},
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@book{Christodoulou2009,
 author={Christodoulou, Demetrios},
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}


@article{Dafermos2003,
  author={Dafermos, Mihalis},
  title={Stability and instability of the {Cauchy} horizon for the spherically symmetric {Einstein--Maxwell--scalar} field equations},
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  doi={10.4007/annals.2003.158.875}
}


@article{Dafermos2005,
  author={Dafermos, Mihalis},
  title={The interior of charged black holes and the problem of uniqueness in general relativity},
  journal={Communications on Pure and Applied Mathematics}, volume={58}, year={2005}, pages={445--504},
  eprint={gr-qc/0307013}, archivePrefix={arXiv},
  url={https://arxiv.org/abs/gr-qc/0307013v3}
}


@article{DafermosLuk2025,
  author={Dafermos, Mihalis and Luk, Jonathan},
  title={The interior of dynamical vacuum black holes {I}: The {$C^0$}-stability of the {Kerr Cauchy} horizon},
  journal={Annals of Mathematics}, volume={202}, number={2}, year={2025}, pages={309--630},
  doi={10.4007/annals.2025.202.2.1}, note={Preprint first posted in 2017}
}


@article{GerochTraschen1987,
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@article{Kerr1963,
  author = {Kerr, Roy P.},
  title = {Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics},
  journal = {Physical Review Letters},
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}


@article{LeFlochMardare2007,
 author={LeFloch, Philippe G. and Mardare, Cristinel},
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}


@article{Luk2018,
  author={Luk, Jonathan}, title={Weak null singularities in general relativity},
  journal={Journal of the American Mathematical Society}, volume={31}, year={2018}, pages={1--63},
  eprint={1311.4970}, archivePrefix={arXiv}, url={https://arxiv.org/abs/1311.4970}
}


@article{LukOh2019I,
  author={Luk, Jonathan and Oh, Sung-Jin},
  title={Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data {I}. The interior of the black hole region},
  journal={Annals of Mathematics}, volume={190}, number={1}, year={2019}, pages={1--111},
  doi={10.4007/annals.2019.190.1.1}
}


@article{LukOh2019II,
  author={Luk, Jonathan and Oh, Sung-Jin},
  title={Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data {II}. The exterior of the black hole region},
  journal={Annals of PDE}, volume={5}, year={2019}, pages={6},
  doi={10.1007/s40818-019-0062-7}
}


@article{Ori1991,
  author={Ori, Amos},
  title={Inner structure of a charged black hole: An exact mass-inflation solution},
  journal={Physical Review Letters}, volume={67}, year={1991}, pages={789--792},
  doi={10.1103/PhysRevLett.67.789}
}


@article{Ori1992,
  author={Ori, Amos},
  title={Structure of the singularity inside a realistic rotating black hole},
  journal={Physical Review Letters}, volume={68}, year={1992}, pages={2117--2120},
  doi={10.1103/PhysRevLett.68.2117}
}


@incollection{Penrose1979,
  author={Penrose, Roger},
  title={Singularities and time-asymmetry},
  editor={Hawking, Stephen W. and Israel, Werner},
  booktitle={General Relativity: An Einstein Centenary Survey},
  publisher={Cambridge University Press}, address={Cambridge},
  year={1979}, pages={581--638}
}


@article{PoissonIsrael1990,
  author={Poisson, Eric and Israel, Werner},
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}


@article{Sbierski2016,
  author = {Sbierski, Jan},
  title = {On the Existence of a Maximal {Cauchy} Development for the {Einstein} Equations: a Dezornification},
  journal = {Annales Henri Poincar{\'e}},
  volume = {17},
  number = {2},
  year = {2016},
  pages = {301--329},
  doi = {10.1007/s00023-015-0401-5},
  eprint = {1309.7591v3},
  archivePrefix = {arXiv},
  primaryClass = {gr-qc},
  url = {https://link.springer.com/article/10.1007/s00023-015-0401-5},
  note = {Published online in 2015; journal issue February 2016}
}


@article{Sbierski2022,
 author={Sbierski, Jan},
 title={On holonomy singularities in general relativity and the {$C^{0,1}_{\mathrm{loc}}$}-inextendibility of spacetimes},
 journal={Duke Mathematical Journal}, volume={171}, number={14},
 pages={2881--2942}, year={2022}, doi={10.1215/00127094-2022-0040},
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}


@article{Sbierski2024Extensions,
 author={Sbierski, Jan},
 title={Uniqueness and non-uniqueness results for spacetime extensions},
 journal={International Mathematics Research Notices}, volume={2024}, number={20},
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 eprint={2208.07752}, archivePrefix={arXiv}
}


@article{Sbierski2026,
 author={Sbierski, Jan},
 title={Lipschitz inextendibility of weak null singularities from curvature blow-up},
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}

@misc{KerrWeakConnection,
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}

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