Heinzle, J. MarkUggla, ClaesLim, Woei Chet2013-01-102013-01-102012-112012Heinzle, J., Uggla, C., & Lim, W. (2012). Spike oscillations. Physical Review D, 86(10), 104049.1550-7998https://hdl.handle.net/10289/7010According to Belinskii., Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatial point evolves independently from its neighbors, in an oscillatory manner that is represented by a sequence of Bianchi type I and II vacuum models. Recent investigations support this conjecture but with a modification: Apart from local BKL behavior there also exists formation of spatial structures ("spikes") at, and in the neighborhood of, certain spatial surfaces that break asymptotic locality; the complete description of a generic spacelike singularity involves spike oscillations, which are described by sequences of Bianchi type I and certain inhomogeneous vacuum models. In this paper we describe how BKL and spike oscillations arise from concatenations of exact solutions in a Hubble-normalized state space setting, suggesting the existence of hidden symmetries and showing that the results of BKL are part of a greater picture.application/pdfenThis article is published in the journal: Physical Review D. (c) 2012 American Physical Society.dynamical-systems approacht-2 symmetric spacetimesgowdy spacetimesmixmaster universevacuum spacetimesrelativistic cosmologyeinstein equationsinhomogeneous cosmologiesasymptotic-behaviorsingularitiesJournal Article10.1103/PhysRevD.86.104049