1998/09/01 by Martin Goliath, Ulf S Nilsson, Claes Uggla · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential equation #Dynamical system (definition) #Dynamical systems theory #Field (mathematics) #Field equation #Field theory (psychology) #Nonlinear Waves and Solitons #gr-qc
paper · pdf · doi:10.1088/0264-9381/15/9/028
published as Class.Quant.Grav.15:2841,1998 · 23 pages, 6 eps-figures
openalex publication_date 1998/09/01 · arxiv created 1998/11/19 · arxiv updated 2010/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems. Using this approach, we obtain a clear picture of the full phase space and the full space of solutions. Solutions of physical interest, e.g. the solution associated with criticality in black hole formation, are easily singled out. We also discuss the various `band structures' that are associated with certain one-parameter sets of solutions.