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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
- Control Number
- 0017161785
- International Standard Book Number
- 9798382807065
- Dewey Decimal Classification Number
- 510
- Main Entry-Personal Name
- Unger, Ryan.
- Publication, Distribution, etc. (Imprint
- [S.l.] : Princeton University., 2024
- Publication, Distribution, etc. (Imprint
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- Physical Description
- 373 p.
- General Note
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- General Note
- Advisor: Dafermos, Mihalis.
- Dissertation Note
- Thesis (Ph.D.)--Princeton University, 2024.
- Summary, Etc.
- 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.
- Subject Added Entry-Topical Term
- Mathematics.
- Subject Added Entry-Topical Term
- Theoretical physics.
- Subject Added Entry-Topical Term
- Astrophysics.
- Subject Added Entry-Topical Term
- Thermodynamics.
- Index Term-Uncontrolled
- Black holes
- Index Term-Uncontrolled
- Critical collapse
- Index Term-Uncontrolled
- Black hole thermodynamics
- Index Term-Uncontrolled
- Positive mass theorem
- Index Term-Uncontrolled
- Scalar curvature
- Index Term-Uncontrolled
- Third law
- Added Entry-Corporate Name
- Princeton University Mathematics
- Host Item Entry
- Dissertations Abstracts International. 85-12B.
- Electronic Location and Access
- 로그인을 한후 보실 수 있는 자료입니다.
- Control Number
- joongbu:654768
MARC
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■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[S.l.]▼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.
