eprintid: 36121
rev_number: 23
eprint_status: archive
userid: 8807
dir: disk0/00/03/61/21
datestamp: 2025-02-25 13:54:46
lastmod: 2025-03-17 12:43:27
status_changed: 2025-02-25 13:54:46
type: doctoralThesis
metadata_visibility: show
creators_name: Bañón Pérez, Pablo
title: Geometric Algebra in General Relativity: A Tetrad-Based
Formalism for Rotating Systems. With Applications to Rotational Dynamics and Black Hole Precession
subjects: ddc-500
subjects: ddc-510
subjects: ddc-530
divisions: i-130200
adv_faculty: af-13
keywords: Geometric Algebra, Clifford Algebra
cterms_swd: Physics
cterms_swd: Gravitation
cterms_swd: Mathematics
cterms_swd: New Mathematics
cterms_swd: Geometrodynamics
cterms_swd: Black Hole
abstract: In this thesis, I develop a novel framework for General Relativity (GR) by combining tetrads with Geometric Algebra (GA), addressing some of the limitations present in traditional formalisms. GR is an inherently geometric theory, yet its conceptual clarity is often obscured by complicated notation and formalism. Tensor calculus, for instance, focuses on component-wise calculations rather than the abstract geometric structure of objects, while differential forms suffer from cumbersome notation and insufficient geometrical interpretation.
		
The motivation behind this novel approach stems from the success GA has shown in other areas of physics, combined with the underutilized use of tetrads in place of traditional coordinate frames. The reliance on coordinate frames unnecessarily complicates expressions and obscures physical insights. By leveraging tetrads within GA, I introduce a more intuitive and powerful approach to GR, offering clearer interpretations and computational advantages. These benefits are demonstrated through applications to FRW spacetimes, the Raychaudhuri equation, and precessing gyroscopes around black holes.
		
This new formalism captures the underlying geometry of physical objects in a more compact, intuitive, and computationally efficient manner. A key advantage lies in the geometric product, which naturally generalizes complex numbers to spaces of arbitrary dimension and signature. This greatly simplifies the treatment of Lorentz transformations, as exemplified in the case of gyroscopic precession. Here, the novel approach reduces the problem from solving a set of four coupled partial differential equations to a single, trivial differential equation in flat spacetime.
		
This thesis lays the groundwork for further exploration of GA in GR, offering new tools that could enhance both theoretical understanding and practical computations in the field.
date: 2025
id_scheme: DOI
id_number: 10.11588/heidok.00036121
ppn_swb: 1919914048
own_urn: urn:nbn:de:bsz:16-heidok-361213
date_accepted: 2025-02-05
advisor: HASH(0x55e83b3fb540)
language: eng
bibsort: BANONPEREZGEOMETRICA
full_text_status: public
place_of_pub: Heidelberg
citation:   Bañón Pérez, Pablo  (2025) Geometric Algebra in General Relativity: A Tetrad-Based Formalism for Rotating Systems. With Applications to Rotational Dynamics and Black Hole Precession.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/36121/1/PhD_Thesis_Pablo%20Ban%CC%83o%CC%81n%20Pe%CC%81rez.pdf