@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},
  note = {\href{https://doi.org/10.1007/BF01645389}{doi:10.1007/BF01645389}}
}

@book{Christodoulou2009,
  author = {Christodoulou, Demetrios},
  title = {The Formation of Black Holes in General Relativity},
  series = {EMS Monographs in Mathematics},
  publisher = {European Mathematical Society},
  address = {Z{\"u}rich},
  year = {2009},
  doi = {10.4171/068},
  url = {https://ems.press/books/emm/62},
  note = {\href{https://doi.org/10.4171/068}{doi:10.4171/068}}
}

@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},
  url = {https://annals.math.princeton.edu/2025/202-2/p01},
  note = {\href{https://doi.org/10.4007/annals.2025.202.2.1}{doi:10.4007/annals.2025.202.2.1}}
}

@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},
  year = {2022},
  pages = {2881--2942},
  doi = {10.1215/00127094-2022-0040},
  url = {https://arxiv.org/abs/2007.12049v2},
  note = {\href{https://doi.org/10.1215/00127094-2022-0040}{doi:10.1215/00127094-2022-0040}}
}

@article{Sbierski2026,
  author = {Sbierski, Jan},
  title = {Lipschitz inextendibility of weak null singularities from curvature blow-up},
  journal = {Inventiones mathematicae},
  volume = {243},
  year = {2026},
  pages = {961--991},
  doi = {10.1007/s00222-025-01387-0},
  url = {https://link.springer.com/article/10.1007/s00222-025-01387-0},
  note = {\href{https://doi.org/10.1007/s00222-025-01387-0}{doi:10.1007/s00222-025-01387-0}}
}

@misc{Gurriaran2026,
  author = {Gurriaran, Sebastian},
  title = {Non-linear instability of the {Kerr Cauchy} horizon near {$i_+$}},
  year = {2026},
  howpublished = {\href{https://arxiv.org/abs/2603.17911v2}{arXiv:2603.17911v2}},
  url = {https://arxiv.org/abs/2603.17911v2},
  note = {Revised 23 March 2026}
}

@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},
  howpublished = {\href{https://arxiv.org/abs/2604.04877v1}{arXiv:2604.04877v1}},
  url = {https://arxiv.org/abs/2604.04877v1},
  note = {Submitted 6 April 2026}
}

@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  = {\href{https://arxiv.org/abs/2506.21183v1}{arXiv:2506.21183v1}},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  doi           = {10.48550/arXiv.2506.21183},
  url           = {https://arxiv.org/abs/2506.21183v1},
  note          = {Submitted 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/},
  note = {\href{https://doi.org/10.5802/aif.3005}{doi: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},
  note = {\href{https://doi.org/10.4171/JST/171}{doi:10.4171/JST/171}}
}

@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},
  note = {\href{https://doi.org/10.1007/BF02392131}{doi:10.1007/BF02392131}}
}

@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},
  note={Reprint of the 1969 article}
}

@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},
  title={Internal structure of black holes},
  journal={Physical Review D}, volume={41}, year={1990}, pages={1796--1809},
  doi={10.1103/PhysRevD.41.1796}
}

@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}
}

@article{Dafermos2003,
  author={Dafermos, Mihalis},
  title={Stability and instability of the {Cauchy} horizon for the spherically symmetric {Einstein--Maxwell--scalar} field equations},
  journal={Annals of Mathematics}, volume={158}, number={3}, year={2003}, pages={875--928},
  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{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{GerochTraschen1987,
 author={Geroch, Robert and Traschen, Jennie},
 title={Strings and other distributional sources in general relativity},
 journal={Physical Review D}, volume={36}, number={4},
 pages={1017--1031}, year={1987}, doi={10.1103/PhysRevD.36.1017},
 url={https://doi.org/10.1103/PhysRevD.36.1017}
}

@article{LeFlochMardare2007,
 author={LeFloch, Philippe G. and Mardare, Cristinel},
 title={Definition and stability of {Lorentzian} manifolds with distributional curvature},
 journal={Portugaliae Mathematica}, volume={64}, number={4},
 pages={535--573}, year={2007}, doi={10.4171/PM/1794},
 url={https://doi.org/10.4171/PM/1794},
 eprint={0712.0122}, archivePrefix={arXiv}
}

@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},
 howpublished={\href{https://arxiv.org/abs/2609.05167v1}{arXiv:2609.05167v1}},
 note={Submitted September 4, 2026}
}

@misc{KerrCTwo,
  author = {{OpenAI}},
  title = {{Quantitative Near-Kerr Evolution and Generic $C^2$ Future Inextendibility}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf}{OAI:Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026}},
  year = {2026}
}

@misc{KerrCOne,
  author = {{OpenAI}},
  title = {{Generic $C^1$ Future Inextendibility Near Rotating Subextremal Kerr Spacetimes}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf}{OAI:Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026}},
  year = {2026}
}

@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}
}

@incollection{Ralston1982,
  author = {Ralston, James},
  title = {{Gaussian} Beams and the Propagation of Singularities},
  editor = {Littman, Walter}, booktitle = {Studies in Partial Differential Equations},
  series = {MAA Studies in Mathematics}, volume = {23},
  publisher = {Mathematical Association of America}, address = {Washington, DC},
  pages = {206--248}, year = {1982}
}

@article{Tanushev2008,
  author = {Tanushev, Nicolay M.},
  title = {Superpositions and Higher Order {Gaussian} Beams},
  journal = {Communications in Mathematical Sciences}, volume = {6}, number = {2},
  pages = {449--475}, year = {2008}
}

@article{LiuRunborgTanushev2013,
  author = {Liu, Hailiang and Runborg, Olof and Tanushev, Nicolay M.},
  title = {Error Estimates for {Gaussian} Beam Superpositions},
  journal = {Mathematics of Computation}, volume = {82}, number = {282},
  pages = {919--952}, year = {2013}, doi = {10.1090/S0025-5718-2012-02656-1},
  url = {https://doi.org/10.1090/S0025-5718-2012-02656-1},
  eprint = {1008.1320}, archivePrefix = {arXiv}
}

@article{CorvinoSchoen2006,
  author = {Corvino, Justin and Schoen, Richard M.},
  title = {On the Asymptotics for the Vacuum {Einstein} Constraint Equations},
  journal = {Journal of Differential Geometry},
  volume = {73}, number = {2}, pages = {185--217}, year = {2006},
  doi = {10.4310/jdg/1146169910}, url = {https://doi.org/10.4310/jdg/1146169910},
  eprint = {gr-qc/0301071}, archivePrefix = {arXiv}
}

@book{ChruscielDelay2003,
  author = {Chru{\'s}ciel, Piotr T. and Delay, Erwann},
  title = {On Mapping Properties of the General Relativistic Constraints Operator in Weighted Function Spaces, with Applications},
  series = {M{\'e}moires de la Soci{\'e}t{\'e} Math{\'e}matique de France, Nouvelle s{\'e}rie},
  number = {94}, publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France}, year = {2003},
  doi = {10.24033/msmf.407}, url = {https://doi.org/10.24033/msmf.407}
}

@article{Carter1968,
  author={Carter, Brandon},
  title={Global structure of the {Kerr} family of gravitational fields},
  journal={Physical Review}, volume={174}, number={5}, year={1968}, pages={1559--1571},
  doi={10.1103/PhysRev.174.1559}
}