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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01t722hd18k
Title: The extremal collapse threshold and the third law of black hole thermodynamics
Authors: Unger, Ryan
Advisors: Dafermos, Mihalis
Contributors: Mathematics Department
Keywords: Black holes
Critical collapse
Extremal
Positive mass theorem
Scalar curvature
Third law
Subjects: Mathematics
Theoretical physics
Issue Date: 2024
Publisher: Princeton, NJ : Princeton University
Abstract: In 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–Nordström 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–Nordström 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.
URI: http://arks.princeton.edu/ark:/88435/dsp01t722hd18k
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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