49. Piotr T. Chru¶ciel, Sebastian J. Szybka On the Ernst electrovacuum equations and ergosurfaces Acta Phys. Pol., B , vol. 39, pp. 5975 (2008). [abstract] [preprint] [journal] 
Abstract: The question of smoothness at the ergosurface of the spacetime
metric constructed out of solutions (E,phi) of the Ernst electrovacuum 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 zerolevelset of f. Some partial results are obtained in the remaining cases: in particular we give examples of leadingorder solutions with singular isolated ``ergocircles". 
50. 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 cohomogeneitytwo triaxial Bianchi typeIX ansatz. In other words, we show that a flip of the wings of a butterfly may influence the process of the black hole formation. 
51. Andrzej Woszczyna Dispersion of density waves in the Universe with positive cosmological constant Conference report (2008). [abstract] [Mathematica 5.2] 
Abstract: Marie Curie Host Fellowships for the Transfer of Knowledge (TOK)
Project MTKDCT2005029466: PARTICLE PHYSICS AND COSMOLOGY: THE INTERFACE,
Fourth Workshop 13.02  16.02.2008, Warszawa 
52. Sebastian J. Szybka Chaos, Gravity and Wave Maps with Target SU(2) Proceedings of the MG11 Meeting on General Relativity (2008). [abstract] [journal] 
Abstract: We present the numerical evidence for chaotic solutions and fractal threshold behavior in the Einstein equations coupled to a wave map (with target SU(2)). This phenomenon is explained in terms of heteroclinic intersections. 
53. Leszek M. Sokołowski Metric gravity theories and cosmology: I. Physical interpretation and viability. Class. Quantum Grav., vol. 24, pp. 33913411 (2007). [abstract] [preprint] 
Abstract: We critically review some concepts underlying current applications of gravity theories with Lagrangians depending on the full Riemann tensor to cosmology. We argue that it is impossible to reconstruct the underlying Lagrangian from the observational data: the RobertsonWalker spacetime is so simple and "flexible" that any cosmic evolution may be fitted by infinite number of Lagrangians. Confrontation of a solution with the astronomical data is obstructed by the existence of many frames of dynamical variables and the fact that initial data for the gravitational triplet depend on which frame is minimally coupled to ordinary matter. Prior to any application it is necessary to establish physical contents and viability of a given gravity theory. A theory may be viable only if it has a stable ground state. We provide a method of checking the stability and show in eleven examples that it works effectively.

54. Leszek M. Sokołowski Metric gravity theories and cosmology: II. Stability of a ground state in f(R) theories. Class. Quantum Grav., vol. 24, pp. 37133734 (2007). [abstract] [preprint] 
Abstract: A fundamental criterion of viability of any gravity theory is existence of a stable groundstate solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary. 