Smooth Gowdy symmetric generalized Taub-NUT solutions

Abstract

We study a class of S3 Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy symmetric generalized Taub-NUT solutions. In particular, we prove existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. The result of our investigations is that a future Cauchy horizon exists for generic asymptotic data. Moreover, we derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about S2xS1 Gowdy models.

56 pages, 1 figure. The new version contains a detailed explanation of the Fuchsian method on the 2-sphere

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• Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
• Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
• An exact smooth Gowdy-symmetric generalized Taub-NUT solution
• Fully pseudospectral time evolution and its application to 1+1 dimensional physical problems
• Wave equations with initial data on compact Cauchy horizons
• Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0\le K<1/3$
• A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes
• Gowdy-symmetric cosmological models with Cauchy horizons ruled by non-closed null generators
• The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary
• Smooth Gowdy-symmetric generalised Taub-NUT solutions in Einstein-Maxwell theory
• Flux quantization in dilatonic Taub-NUT dyons
• Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor
• Smooth Gowdy-symmetric generalised Taub-NUT solutions with polynomial initial data
• Exact solutions and their interpretation - session A1