Some problems on prescribed mean curvature and kinematics in general relativity

Abstract

La tesis está estructurada en dos bloques. El primero de ellos se ocupa del problema de la prescripción de la función curvatura media de grafos espaciales, rotacionalmente simétricos y embebidos en ciertos espaciotiempos de relevancia física, como el de Schwarzschild, el de Reissner-Nordström, o los de Friedmann-Lemaître-Robertson-Walker. En la segunda parte, varios conceptos cinemáticos, bien conocidos en la física clásica, se transportan al ámbito de la Relatividad General.

This thesis maybe structured into two blocks. In the first part we deal with the problem of the mean curvature prescription function of spatial graphs, which are rotationally symmetrical and embedded in certain space time of physical relevance, such as chwarzschild, Reissner-Nordström, or Friedmann-Lematrîe-Robertson-Walker. In the second part, several kinematic concepts, well known in classical physics, are transposed into the realm of General Relativity.