2002/03/12 by James Isenberg, Vincent Moncrief, Vince Moncrief
Physics and Astronomy · #Black Holes and Theoretical Physics #Class (philosophy) #Cosmology and Gravitation Theories #Covariant transformation #Einstein #Isometry group #Noncommutative and Quantum Gravity Theories #Polarization (electrochemistry) #Set (abstract data type) #Singularity #gr-qc
paper · pdf · doi:10.1088/0264-9381/19/21/305
published as Class.Quant.Grav. 19 (2002) 5361-5386 · 42 pges
arxiv created 2002/03/12 · openalex publication_date 2002/10/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use the Fuchsian algorithm to study the behaviour near the singularity of certain families of U (1) symmetric solutions of the vacuum Einstein equations (with the U (1) isometry group acting spatially). We consider an analytic family of polarized solutions with the maximum number of arbitrary functions consistent with the polarization condition (one of the 'gravitational degrees of freedom' is turned off) and show that all members of this family are asymptotically velocity term dominated (AVTD) as one approaches the singularity. We show that the same AVTD behaviour holds for a family of 'half-polarized' solutions, which is defined by adding one extra arbitrary function to those characterizing the polarized solutions. (The full set of nonpolarized solutions involves two extra arbitrary functions.) Using SL (2, R ) Geroch transformations, we produce a further class of U (1) symmetric solutions with AVTD behaviour. We begin to address the issue of whether AVTD behaviour is independent of the choice of time foliation by showing that indeed AVTD behaviour is seen for a wide class of choices of harmonic time in the polarized and half-polarized ( U (1) symmetric vacuum) solutions discussed here.