MG11 
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Abstract

Axially symmetric equilibrium regions of FLRW universes

The study of the matching of stationary and axisymmetric spacetimes with Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes preserving the axial symmetry is presented. We show, in particular, that any orthogonally transitive stationary and axisymmetric region in FLRW must be static, irrespective of the matter content. Therefore, previous results on static regions in FLRW cosmologies apply. As a result, the only stationary and axisymmetric vacuum region that can be matched to a (non-static) FLRW spacetime is a spherically symmetric region of Schwarzschild. This constitutes another uniqueness result for the Einstein–Straus model (as well as its Oppenheimer–Snyder counterpart), and hence another indication of its unsuitability as an answer to the influence of the cosmic expansion on local physics.

Bounds for scalar waves and linear perturbations on self-similar naked-singularity backgrounds

The stability of naked singularities in self-similar collapse is probed using scalar waves. It is shown that the multipoles of a minimally coupled massless scalar field propagating on a spherically symmetric self-similar background space-time admitting a naked singularity maintain finite $H^{1,2}$ norm as they impinge on the Cauchy horizon. It is also shown that each multipole obeys a pointwise bound at the horizon, as does its locally observed energy density. $H^{1,2}$ and pointwise bounds are also obtained for the multipoles of a minimally coupled massive scalar wave packet. We discuss the extension of these results to odd-parity linear perturbations of the space-time.