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  

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Control Number  

joongbu:654768