Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Oikonomidis Filippos
Supervisors info:
Παναγιώτης Γιαννιώτης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ, (επιβλέπων),
Θεοχάρης Αποστολάτος Αναπλ. Καθηγητής Τμήμα Φυσικής ΕΚΠΑ,
Διονύσιος Λάππας Αναπλ. Καθηγητής Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Black Hole Uniqueness Theorems in the Theory of General Relativity
Translated title:
Black Hole Uniqueness Theorems in the Theory of General Relativity
Summary:
In this thesis we provide a detailed proof of Israel’s uniqueness theorem of the Schwarzschild solution in the more general setting proven by Bunting and Masood-ul-Alam. The methods used in the proof of the generalized uniqueness theorem has had an important impact in many later proofs such as higher dimensional analogs of uniqueness theorems for the Schwarzschild solution and the Riemannian Penrose inequality by Bray. General relativity is the best theory so far describing gravity together with Einstein’s equation which relates the spacetime geometry to the matter distribution. One of the most important exact solutions of Einstein’s equation is the Schwarzschild solution. It describes the exterior gravitational field of a static, spherically symmetric body, it predicts several phenomena of general relativity in our solar system and for a massive, spherical body that has gravitationally collapsed it describes the spacetime in vacuum which contains a singularity within a black hole.
After showing some facts for Lorentzian geometry and special relativity, we prove Birkhoff’s theorem, that the Schwarzschild metric is the unique spherical solution in vacuum, and describe the Kruskal coordinates which extends the Schwarzschild metric to the whole spacetime with a singularity. Afterwards we show what are the initial data for the well-posedness of the Einstein’s equation in vacuum and their constraint equations. At last we prove that the Schwarzschild metric is the unique static, asymptotically flat, vacuum spacetime with regular event horizon without assuming that the event horizon is connected.
Main subject category:
Science
Keywords:
asymptotically flat spacetime, spherically symmetric spacetime, static spacetime, Schwarzschild metric, Black hole uniqueness theorems, positive mass theorem
