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Identifier

000467710

Title

The near-horizon geometry of the extremal Kerr black hole with higher curvature corrections

Alternative Title

Η γεωμετρία κοντά στον ορίζοντα της ακραίας μελανής οπής Kerr με διορθώσεις υψηλότερης καμπυλότητας

Author

Κουτσάκης, Ευάγγελος Κ.

Thesis advisor

Πορφυριάδης, Αχιλλέας

Reviewer

Νιάρχος, Βασίλειος
Rosen, Christopher

Abstract

It was recently shown that effective field theory breaks down near the horizon of an extremal Kerr black hole. Higher derivative terms added to the Einstein-Hilbert action which were thought to produce small corrections in regions of low energy, generate curvature singularities on the extremal horizon. Upon generalizing the near-horizon metric to the effective theory, generic stationary, axisymmetric perturbations are introduced to extend the near horizon geometry to an asymptotically flat spacetime. It is these tidal deformations that are responsible for the divergent behavior. The question of whether this breakdown indicates a region where signatures of new physics may be discovered, remains open. The present work aims to provide a comprehensive review of all the above, beginning from scratch. Upon reviewing fundamental concepts of General Relativity relevant to this topic, the Kerr spacetime and its features are systematically studied. What follows is a demonstration of why effective field theory is employed, the physical and mathematical reasons constraining its formulation, and the methodology of constructing a gravitational effective theory. Then, starting from a metric ansatz for the near-horizon geometry, the corresponding Einstein equations are derived. The leading-order solutions, determined in the literature, are plugged in and are found to contain a typographical error. It is a minus sign that should have been a plus. Finally, certain parity-violating theories have not been studied in the literature, at least for black hole solutions. In the last section of this work, an attempt is made to repeat the previous methodology for an effective Lagrangian containing parity-violating terms. Hardware limitations prevent significant progress. A repository containing all relevant Mathematica notebooks for this work can be found at https://github.com/VaggelisKt/Master-s-Thesis-Notebooks.

Language

English

Subject

EFT

Effective field theory

General relativity

NHEK

Tidal deformations

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