2014/04/01 by William Almonacid, Almonacid, William
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1404.1045
openalex publication_date 2014/04/01 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
The dynamics of extended bodies is a fundamental problem in any gravitational\ntheory. In the case of General Relativity, this problem is under study since\nthe theory was published. Several methods have been developed and different\napproaches are avalaible in the literature to interpret the relativistic\ncontributions in the motion under gravity influence. The main goal in this\nthesis is to study a general method to face the equation of motion for extended\nbodies in General Relativity. We started with a proposal in the Newtonian\ntheory, which consists in a multipolar expansion for the gravitational\npotentials as a function of the mass density moments and other physical\nvariables as the stress tensor. The methodology give us the equation of motion\nfor an isolated and self-gravitating system of extended bodies in Newtonian\nmechanics. A geometrical approach to get the equation of motion is also used\nfor the Newtonian problems, it allows us to extend the methodology to General\nRelativity. In General Relativity, some new concepts are necessary: world tube,\nworld line, generalized ideas of momentum, angular momentum, torque and center\nof mass are introduced in a general context. General expressions for the\nequation of motion in the case of extended bodies are written without any\nrestriction. In order to gain some physical understanding, we compute the\nPapapetrous's equation of motion for a test extended body in a static and\nisotropic metric. Finally, we study a system of two extended bodies in the\npost-Newtonian approximation. We define the mass multipole moments and momentum\nfrom the gravitational potentials (metric functions) to the first\npost-Newtonian order. We follow the Landau-Liftshitz formalism to find out the\nequation of motion for the moments and applying the standard coordinate\ntransformation for this theory, we write the traslational equation of motion.\n