13. Piotr T. Chru¶ciel, 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. Chru¶ciel, 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. |