13. Piotr T. Chruściel, Michał Eckstein, Sebastian J. Szybka
On smoothness of Black Saturns
Journal of High Energy Physics, vol. 2010, pp. 1-39 (2010).
[abstract] [preprint] [journal]

Abstract:
We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R x S^3 and R x S^1 x S^2. We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.

14. Piotr T. Chruściel, Sebastian J. Szybka
On the Ernst electro-vacuum equations and ergosurfaces
Acta Phys. Pol., B , vol. 39, pp. 59-75 (2008).
[abstract] [preprint] [journal]

Abstract:
The question of smoothness at the ergosurface of the space-time metric constructed out of solutions (E,phi) of the Ernst electro-vacuum equations is considered. We prove smoothness of those ergosurfaces at which Re(E) provides the dominant contribution to f=-(Re(E)+|phi|^2) at the zero-level-set of f. Some partial results are obtained in the remaining cases: in particular we give examples of leading-order solutions with singular isolated ``ergocircles".

15. Sebastian J. Szybka, Tadeusz Chmaj
Fractal Threshold Behavior in Vacuum Gravitational Collapse
Phys. Rev. Lett., vol. 100, p. 101102 (2008).
[abstract] [preprint] [journal] [download]

Abstract:
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.

16. P. T. Chrusciel, G. M. Greuel, R. Meinel, S. J. Szybka
The Ernst equation and ergosurfaces
Class. Quantum Grav., vol. 23, pp. 4399-4414 (2006).
[abstract] [preprint] [journal]

Abstract:
We show that analytic solutions $\mcE$ of the Ernst equation with non-empty zero-level-set of $\Re \mcE$ lead to smooth ergosurfaces in space-time. In fact, the space-time metric is smooth near a "Ernst ergosurface" $E_f$ if and only if $\mcE$ is smooth near $E_f$ and does not have zeros of infinite order there.

17. P. Bizoń, S. J. Szybka, A. Wassserman
Periodic self-similar wave maps coupled to gravity
Phys. Rev. D, vol. 69, p. 064014 (2004).
[abstract] [preprint] [journal]

Abstract:
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.

18. S. J. Szybka
Chaotic self-similar wave maps coupled to gravity
Phys. Rev. D, vol. 69, p. 084014 (2004).
[abstract] [preprint] [journal]

Abstract:
We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. For some values of the coupling constant we present numerical evidence for the chaotic solution and the fractal threshold behavior. We explain this phenomenon in terms of horseshoe-like dynamics and heteroclinic intersections.