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Title: | Birkhoff’s theorem for Einstein gravity and beyond |
Author: | Rodríguez Amado, Emilio |
Director/Tutor: | Bueno Gómez, Pablo |
Keywords: | Teorema de Birkhoff Equacions de camp d'Einstein Treballs de fi de grau Birkhoff's theorem Einstein field equations Bachelor's theses |
Issue Date: | Jun-2023 |
Abstract: | Birkhoff’s theorem establishes that any spherically symmetric vacuum solution of Einstein’s equations is necessarily static and uniquely given by the Schwarzschild metric. In this TFG we prove this theorem for Einstein gravity and several of its extensions, which include the presence of electric charge as well as higher-curvature terms in the action. More precisely, we explicitly prove Birkhofflike theorems for: Einstein, Einstein-Maxwell, Einstein-Gauss-Bonnet and Einstein-Maxwell-Gauss-Bonnet theories in general dimensions. In all cases, starting from a general spherically symmetric ansatz, we are able to show that the equations of motion impose the staticity condition, and fully constrain the metric to take the form of the unique static and spherically symmetric spacetime of each theory. We also comment on the validity of the theorem for general Lovelock theories and its current status for more general higher-curvature theories of gravity |
Note: | Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2023, Tutor: Pablo Bueno Gómez |
URI: | http://hdl.handle.net/2445/201782 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Física |
Files in This Item:
File | Description | Size | Format | |
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RODRÍGUEZ AMADO EMILIO_7934142.pdf | 344.83 kB | Adobe PDF | View/Open |
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