KTH/SU Mathematics Colloquium

05-09-14

Jürg Fröhlich, ETH

Boson Stars

Systems of many bosons interacting through Newtonian two-body potentials are considered. The mean-field limit of such systems is studied. A Egorov-type theorem characterizing the mean-field limit in terms of a semi-relativistic Hartree equation is stated and discussed. Subsequently, results on the semi-relativistic Hartree equation are summarized: When the total mass of the system exceeds a certain critical value blow-up after a finite time is encountered; (gravitational collapse of heavy objects). For masses below the critical value, existence of solitons is established, and the dynamics of such solitons in an external potential is studied. These solitons describe stable boson stars with masses roughly the size of the "Matterhorn".