Espacio-tiempo de Sitter (dS) y Anti de Sitter (AdS)-Cálculo e interpretación de los campos de Killing

Abstract

A study based on the General Theory of Relativity is carried out. The physical and geometric properties of two solutions of Einstein's field equations de Sitter (dS) and Anti de Sitter (AdS) are examined. As a starting point, the Einstein-Hilbert action is considered, whose process of variation leads to the equations of the field; These admit multiple solutions depending on the sources of matter and energy. In particular, the solution proposed by William De Sitter describes an empty Universe that contracts to a certain minimum distance of radius R and then enters an exponentially accelerated expansion, called De Sitter Space-Time. The most relevant properties are positive constant curvature, negative cosmological constant (Anti De Sitter AdS) and the symmetric maximality (maximum number of symmetries). Finally, the Killing fields associated with each of the solutions studied are calculated. These are vector fields that indicate the directions in which the metric remains invariant, and have the information related to the symmetries and conserved quantities of the system; as indicated by Noether's theorem.