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We show that analytic solutions E of the Ernst equation with nonempty zero-level-set of RE lead to smooth ergosurfaces in space-time. In fact, the space-time metric is smooth near a “Ernst ergosurface” Ef if and only if E is smooth near Ef and does not have zeros of infinite order there.

We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods we show existence of an unstable periodic solution lying at the boundary between the basins of two generic attractors.

- Sebastian J. Szybka, Tadeusz Chmaj
- Physical review letters
- 2008

We present the numerical evidence for fractal threshold behavior in the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. In other words, we show that a flip of the wings of a butterfly may influence the process of the black hole formation.

The question of smoothness at the ergosurface of the space-time metric constructed out of solutions (E , φ) of the Ernst electro-vacuum equations is considered. We prove smoothness of those ergosurfaces at which RE provides the dominant contribution to f = −(RE + |φ|) at the zero-level-set of f . Some partial results are obtained in the remaining cases: in… (More)

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