München 2006 – wissenschaftliches Programm

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GR: Gravitation und Relativitätstheorie

GR 201: Einstein-Yang-Mills-Higgs, Skyrmionen und Bosonensterne

GR 201.3: Vortrag

Dienstag, 21. März 2006, 11:30–11:50, K

Platonic sphalerons in Einstein-Yang-Mills and Yang-Mills-dilaton theory — •Kari Myklevoll, Burkhard Kleihaus, and Jutta Kunz — Universität Oldenburg

Gravitating classical solutions in Yang-Mills (YM) theories have many suprising properties. For instance, black holes in these theories can possess “hair”, i. e. non-trivial YM fields not corresponding to global charges. In contrast Einstein-Maxwell (EM) black holes are completely determined by their global charges. Moreover in EM theory, all static black holes are spherically symmetric, whereas static axially symmetric black hole solutions have been found in Einstein-Yang-Mills (EYM) theory.

We here present new sphaleron solutions in EYM and Yang-Mills-dilaton theory. These sphalerons have no continuous rotational symmetries at all, but have the symmetries of crystals or of platonic bodies, and we therefore call them platonic sphalerons. Their symmetries are related to certain rational maps of degree N.

Since the gravitating platonic sphalerons are static regular solutions without continuous symmetries, they belong to a completely new kind of gravitating solutions, and most importantly these solutions indicate the existence of static black holes with only discrete symmetries of the horizon.