Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies.pdfVIP

Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies Beverly K. Berger 3 0 Physics Division, National Science Foundation, Arlington, VA 22207 USA 0 2 Abstract. Heuristic arguments and numerical simulations support the Belinskii et c e al (BKL) claim that the approach to the singularity in generic gravitational collapse is D characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in 0 collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of 2 one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the 1 variables of U (1)-symmetric cosmologies are reviewed. Similar constructions for U (1)- v 2 5 symmetric spacetimes in terms of the dynamics of generic T -symmetric spacetime are 9 presented. 0 2 1 3 0 1. Introduction / c q- Vincent Moncrief and I became interested in spatially inhomogeneous cosmological r g spacetimes as graduate students at the University of Maryland more than 30 years ago. : Kuchar [1] had extended Misner’s minisuperspace approach to quantum cosmology [2] v i X to cylindrically symmetric spacetimes containing gravitational waves (Einstein-Rosen r waves [3]). At the same time, Gowdy had recognized that essentially interchanging a the radial and time coordinates in the Einstein-Rosen solution yielded cosmological spacetimes containing gravitational waves [4]. Moncr