Publication: Geometric structures and causality in the space of ligth rays of a spacetime
Loading...
Files
Official URL
Full text at PDC
Publication Date
2017-05-24
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Complutense de Madrid
Citations
Exportar
Abstract
Inspirado por algunos de los ḿas grandes mateḿaticos del siglo XIX y principios del XX como Felix Klein, Julius Pl¨ucker, Arthur Cayley and Sophus Lie entre otros, R. Penrose desarrolĺo, en las d́ecadas de 1960 y 1970, el programa twistor [56], [58]. Esta teoŕıa est́a motivada en la obtencíon de un formalismo que permita unir la Relatividad general con la F́ısica cúantica. Los espacios Twistor son estructuras complejas que contienen informacíon del espacio–tiempo de Minkowski 4–dimensional de modo que las geod́esicas luz pueden verse como elementos b́asicos (puntos) de esta geometŕıa compleja. Aśı, a partir de este nuevo punto de vista, surje la siguiente idea: los conjuntos de todas las geod́esicas luz que pasan por diferentes puntos, son distintos, o de forma equivalente, si dos observadores contemplan exactamente el mismo cielo, entonces est́an en el mismo punto del espacio–tiempo. Por tanto, en el espacio–tiempo de Minkowski, el conjunto de geod́esicas luz que pasan por un determinado punto, caracteriza dicho punto. A finales de la d́ecada de 1980, R. Low comenźo a trabajar en esta idea aplićandola ḿas tarde a espacio–tiempos generales, no necesariamente minkowskianos, y sobre una variedad diferenciable real. En su trabajo [39], [41], [40], [42], [44], [45] el autor estudia la topoloǵıa y la geometŕıa del espacio de geod́esicas luz (desparametrizadas) y ofrece condiciones para que ́estas tengan buenas propiedades. Adeḿas, apunta la existencia de una estructura de contacto en el espacio de geod́esicas luz y observa que la estructura causal del espacio–tiempo tambíen se halla codificada en dicho espacio N de geod́esicas luz, o rayos de luz como los llamaremos de ahora en adelante. Una structura importante contenida en N es la familia de cielos: el conjunto de todos los rayos de luz que pasan por x se denomina cielo de x y se denota como X. En este trabajo, llamaremos al conjunto de cielos...
Inspired by some of the greatest mathematicians in 19th century and beginning of 20th such as Felix Klein, Julius Pl¨ucker, Arthur Cayley and Sophus Lie among others, R. Penrose in 1960–70s developed the twistor programme [56], [58]. This theory is motivated to set a formalism in order to merge general relativity and quantum physics. Twistor spaces are complex structures containing information of 4–dimensional Minkowski spacetime in such a way null geodesics can be seen as basic elements (points) in this complex geometry. Then, an idea emerges from this new point of view: the sets of all null geodesics passing through different events in the spacetime are different, or equivalently, if two observers watch exactly the same sky, then they are at the same point of the spacetime. So, in Minkowski spacetime, all null geodesics passing through a specific point characterizes said point. In late 1980s, R. Low started to work out this idea and he applied it later for a general spacetime, not necessarily Minkowskian, and in a real differential manifold. In his work [39], [41], [40], [42], [44], [45] the author studies the topology and geometry of the space of (unparametrized) null geodesics and offers conditions for having good properties. He points out the existence of a contact structure in the space of null geodesics and observes that the causal structure of the spacetime is also encoded in said space N of null geodesics, or light rays as we will name them from now on. An important structure contained in N is the family of skies: the set of all light rays passing through x is called the sky of x and is denoted by X...
Inspired by some of the greatest mathematicians in 19th century and beginning of 20th such as Felix Klein, Julius Pl¨ucker, Arthur Cayley and Sophus Lie among others, R. Penrose in 1960–70s developed the twistor programme [56], [58]. This theory is motivated to set a formalism in order to merge general relativity and quantum physics. Twistor spaces are complex structures containing information of 4–dimensional Minkowski spacetime in such a way null geodesics can be seen as basic elements (points) in this complex geometry. Then, an idea emerges from this new point of view: the sets of all null geodesics passing through different events in the spacetime are different, or equivalently, if two observers watch exactly the same sky, then they are at the same point of the spacetime. So, in Minkowski spacetime, all null geodesics passing through a specific point characterizes said point. In late 1980s, R. Low started to work out this idea and he applied it later for a general spacetime, not necessarily Minkowskian, and in a real differential manifold. In his work [39], [41], [40], [42], [44], [45] the author studies the topology and geometry of the space of (unparametrized) null geodesics and offers conditions for having good properties. He points out the existence of a contact structure in the space of null geodesics and observes that the causal structure of the spacetime is also encoded in said space N of null geodesics, or light rays as we will name them from now on. An important structure contained in N is the family of skies: the set of all light rays passing through x is called the sky of x and is denoted by X...
Description
Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Geometría y Tipología, leída el 04-03-2016