[en] We show that the gravitating static soliton in the 2+1 dimensional O(3) σ model does not exist in the presence of a negative cosmological constant, contrary to the claim made by Kim and Moon in [Phys. Rev. D 58, 105013 (1998).]

[en] We present a detailed analytical study of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using a shooting argument, we prove that there is a countable family of solutions which are analytic inside the past self-similarity horizon. In addition, we show that for sufficiently small values of the coupling constant these solutions possess a regular future self-similarity horizon and thus are examples of naked singularities. One of the solutions constructed here has been recently found as the critical solution at the threshold of black-hole formation

[en] We give a very short proof that the vacuum Einstein equations in 4 + 1 dimensions have no cohomogeneity-two Bianchi IX continuously self-similar solutions. (fast track communication)

[en] 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 the existence of an unstable periodic solution lying at the boundary between the basins of two generic attractors