98 research outputs found
Half polarized U(1) symmetric vacuum spacetimes with AVTD behavior
In a previous work, we used a polarization condition to show that there is a
family of U(1) symmetric solutions of the vacuum Einstein equations such that
each exhibits AVTD (Asymptotic Velocity Term Dominated) behavior in the
neighborhood of its singularity. Here we consider the general case of U(1)
bundles and determine a condition, called the half polarization condition,
necessary and sufficient in our context, for AVTD behavior near the
singularity
Global Hyperbolicity and Completeness
We prove global hyperbolicity of spacetimes under generic regularity
conditions on the metric. We then show that these spacetimes are timelike and
null geodesically complete if the gradient of the lapse and the extrinsic
curvature are integrable. This last condition is required only for the
tracefree part of if the universe is expanding.Comment: 7 pages. Accepted for publication in the Journal of Geometry and
Physics. v2: Minor typos correcte
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