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The Extremal Collapse Threshold and the Third Law of Black Hole Thermodynamics
The Extremal Collapse Threshold and the Third Law of Black Hole Thermodynamics
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151445
- ISBN
- 9798382807065
- DDC
- 510
- 저자명
- Unger, Ryan.
- 서명/저자
- The Extremal Collapse Threshold and the Third Law of Black Hole Thermodynamics
- 발행사항
- [Sl] : Princeton University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 373 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Dafermos, Mihalis.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2024.
- 초록/해제
- 요약In this dissertation, we investigate extremal black holes in general relativity. Extremal black holes are exceptional solutions of Einstein's equations which have absolute zero temperature in the celebrated thermodynamic analogy of black hole mechanics.Our first main result is a definitive disproof of the "third law of black hole thermodynamics." We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein-Maxwell-charged scalar field system which are exactly isometric to extremal Reissner-Nordstrom after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. We also prove similar black hole formation results for very slowly rotating Kerr black holes in vacuum.Our second main result is a proof that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal Reissner-Nordstrom black hole. We call this critical phenomenon extremal critical collapse and the present work constitutes the first rigorous result on the black hole formation threshold in general relativity.The above mentioned results constitute Part I of this dissertation and were all obtained in joint work with Christoph Kehle.In Part II of this dissertation, we study extensions of the celebrated positive mass theorem to a very general class of initial data, including extremal black holes. These results were obtained in collaboration with Dan A. Lee, Martin Lesourd, and Shing-Tung Yau. We provide a resolution of the spacetime positive mass theorem on manifolds with boundary, a resolution of the remaining cases of Schoen and Yau's Liouville conjecture for locally conformally flat manifolds, and demonstrate a novel scalar curvature shielding phenomenon for the ADM mass.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical physics
- 일반주제명
- Astrophysics
- 일반주제명
- Thermodynamics
- 키워드
- Black holes
- 키워드
- Scalar curvature
- 키워드
- Third law
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017161785
■00520250211151445
■006m o d
■007cr#unu||||||||
■020 ▼a9798382807065
■035 ▼a(MiAaPQ)AAI31296386
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aUnger, Ryan.▼0(orcid)0000-0002-9226-303X
■24510▼aThe Extremal Collapse Threshold and the Third Law of Black Hole Thermodynamics
■260 ▼a[Sl]▼bPrinceton University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a373 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Dafermos, Mihalis.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2024.
■520 ▼aIn this dissertation, we investigate extremal black holes in general relativity. Extremal black holes are exceptional solutions of Einstein's equations which have absolute zero temperature in the celebrated thermodynamic analogy of black hole mechanics.Our first main result is a definitive disproof of the "third law of black hole thermodynamics." We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein-Maxwell-charged scalar field system which are exactly isometric to extremal Reissner-Nordstrom after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. We also prove similar black hole formation results for very slowly rotating Kerr black holes in vacuum.Our second main result is a proof that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal Reissner-Nordstrom black hole. We call this critical phenomenon extremal critical collapse and the present work constitutes the first rigorous result on the black hole formation threshold in general relativity.The above mentioned results constitute Part I of this dissertation and were all obtained in joint work with Christoph Kehle.In Part II of this dissertation, we study extensions of the celebrated positive mass theorem to a very general class of initial data, including extremal black holes. These results were obtained in collaboration with Dan A. Lee, Martin Lesourd, and Shing-Tung Yau. We provide a resolution of the spacetime positive mass theorem on manifolds with boundary, a resolution of the remaining cases of Schoen and Yau's Liouville conjecture for locally conformally flat manifolds, and demonstrate a novel scalar curvature shielding phenomenon for the ADM mass.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aTheoretical physics
■650 4▼aAstrophysics
■650 4▼aThermodynamics
■653 ▼aBlack holes
■653 ▼aCritical collapse
■653 ▼aBlack hole thermodynamics
■653 ▼aPositive mass theorem
■653 ▼aScalar curvature
■653 ▼aThird law
■690 ▼a0405
■690 ▼a0753
■690 ▼a0596
■690 ▼a0348
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161785▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
