TY - BOOK

T1 - On the Stability of Spherically Symmetric Self-Gravitating Classical and Quantum Systems

AU - Makedonski, Mathias

PY - 2014

Y1 - 2014

N2 - We study the energetic stability of spherically symmetric self-gravitating systems beginning with an extensive review of the literature on perfect fluid bodies in Newtonian gravity with a particular focus on existence and uniqueness results for solutions of the Chandrasekhar equation. Moving on to the description of the corresponding systems in the setting of general relativity, it is shown, that the Tolman-Oppenheimer-Volko equation can be obtained from a suitable variation of the total energy. We prove a previously unnoticed energetic instability of the model. Staying in the general relativistic setting, we examine the self-gravitating massive free scalar eld. It is shown, by proving suitable dierentiability properties of the occurring functionals, that Einstein's equations in this setting can again be obtained by a constrained variation of the total mass as dened by Arnowitt, Deser and Misner. As for the perfect fluid, we prove energetic instability and conclude our investigations by constructing a naive quantum version of the free massive scalar eld, that also suers energetic instability. ´

AB - We study the energetic stability of spherically symmetric self-gravitating systems beginning with an extensive review of the literature on perfect fluid bodies in Newtonian gravity with a particular focus on existence and uniqueness results for solutions of the Chandrasekhar equation. Moving on to the description of the corresponding systems in the setting of general relativity, it is shown, that the Tolman-Oppenheimer-Volko equation can be obtained from a suitable variation of the total energy. We prove a previously unnoticed energetic instability of the model. Staying in the general relativistic setting, we examine the self-gravitating massive free scalar eld. It is shown, by proving suitable dierentiability properties of the occurring functionals, that Einstein's equations in this setting can again be obtained by a constrained variation of the total mass as dened by Arnowitt, Deser and Misner. As for the perfect fluid, we prove energetic instability and conclude our investigations by constructing a naive quantum version of the free massive scalar eld, that also suers energetic instability. ´

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99122037156305763

M3 - Ph.D. thesis

SN - 978-87-7078-962-2

BT - On the Stability of Spherically Symmetric Self-Gravitating Classical and Quantum Systems

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -