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".