Corrigendum to “Stable black holes: In vacuum and beyond”

By Elena Giorgi

Abstract

This note is a corrigendum to the paper by Elena Giorgi [Bull. Amer. Math. Soc. 60 (2023), no. 1, 1–27] pointing out a misrepresentaton of the “Collapse conjecture”, which was proved by Christodoulou [The formation of black holes in general relativity, EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2009].

In Section 3 of Reference 3 the characterization of the mathematical problem of gravitational collapse as the “Collapse conjecture” is incorrect. The first proof of formation of closed trapped surfaces, and eventually black holes, through the focusing of incoming gravitational waves for the Einstein vacuum equation was obtained in a breakthrough result by Christodoulou Reference 2 in 2009.

For more details about black hole formation, we refer to the survey paper by Bieri Reference 1.

Table of Contents

  1. Abstract
  2. Untitled Section

References

Reference [1]
Lydia Bieri, Black hole formation and stability: a mathematical investigation, Bull. Amer. Math. Soc. (N.S.) 55 (2018), no. 1, 1–30, DOI 10.1090/bull/1592. MR3737208,
Show rawAMSref \bib{Bieri}{article}{ author={Bieri, Lydia}, title={Black hole formation and stability: a mathematical investigation}, journal={Bull. Amer. Math. Soc. (N.S.)}, volume={55}, date={2018}, number={1}, pages={1--30}, issn={0273-0979}, review={\MR {3737208}}, doi={10.1090/bull/1592}, }
Reference [2]
Demetrios Christodoulou, The formation of black holes in general relativity, EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2009, DOI 10.4171/068. MR2488976,
Show rawAMSref \bib{Christo}{book}{ author={Christodoulou, Demetrios}, title={The formation of black holes in general relativity}, series={EMS Monographs in Mathematics}, publisher={European Mathematical Society (EMS), Z\"{u}rich}, date={2009}, pages={x+589}, isbn={978-3-03719-068-5}, review={\MR {2488976}}, doi={10.4171/068}, }
Reference [3]
Elena Giorgi, Stable black holes: in vacuum and beyond, Bull. Amer. Math. Soc. (N.S.) 60 (2023), no. 1, 1–27, DOI 10.1090/bull/1781. MR4520774,
Show rawAMSref \bib{Bull}{article}{ author={Giorgi, Elena}, title={Stable black holes: in vacuum and beyond}, journal={Bull. Amer. Math. Soc. (N.S.)}, volume={60}, date={2023}, number={1}, pages={1--27}, issn={0273-0979}, review={\MR {4520774}}, doi={10.1090/bull/1781}, }

Article Information

MSC 2020
Primary: 83C05 (Einstein’s equations (general structure, canonical formalism, Cauchy problems)), 83C22 (Einstein-Maxwell equations), 83C57 (Black holes), 83C50 (Electromagnetic fields in general relativity and gravitational theory), 35A01 (Existence problems for PDEs: global existence, local existence, non-existence)
Author Information
Elena Giorgi
Department of Mathematics, Columbia University
elena.giorgi@columbia.edu
ORCID
MathSciNet
Journal Information
Bulletin of the American Mathematical Society, Volume 60, Issue 3, ISSN 1088-9485, published by the American Mathematical Society, Providence, Rhode Island.
Publication History
This article was received on and published on .
Copyright Information
Copyright 2023 American Mathematical Society
Article References
  • Permalink
  • Permalink (PDF)
  • DOI 10.1090/bull/1797
  • MathSciNet Review: 4588045
  • Show rawAMSref \bib{4588045}{article}{ author={Giorgi, Elena}, title={Corrigendum to ``Stable black holes: In vacuum and beyond''}, journal={Bull. Amer. Math. Soc.}, volume={60}, number={3}, date={2023-07}, pages={407-407}, issn={0273-0979}, review={4588045}, doi={10.1090/bull/1797}, }

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