The languages of spacetime

• Autor(a) principal: Felipe Brandão Guisoli
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/58363
• topic: Relatividade geral; Gravitação; Formalismo hamiltoniano; Variáveis de Ashtekar; Gravitação quântica de laços; Relatividade geral; Gravitação

The theory of general relativity emerges in 1915, and its mathematical stage is a four-dimensional Lorentzian manifold. Our goal will be to explore different languages and formulations of the theory, with different quantities playing the role of dynamical variables. We will start with the original formulation of the theory developed by Einstein, and then pass to the Lagrangian formulation, first developed by Hilbert. Then we will develop two Hamiltonian formulations of gravity, based on a (3+1) foliation of spacetime. The first will be done with the three-dimensional spatial metric as dynamical variable. Such a formalism is known as the ADM formalism of general relativity and allows for the construction of a Hamiltonian for the theory in terms of constraints and Lagrange multipliers. Finally, we will analyze the Hamiltonian formalism based on the Holst action, in terms of Ashtekar variables. This formulation provides a possible path for the canonical quantization of the gravitational field, in the approach known as loop quantum gravity.