Self-interaction potential

3.6 Self-interaction potential

An example of the richer phenomenology in the presence of a scale in the field equations is the spherical massive scalar field with a potential $m2 ϕ2$ [34

] coupled to gravity: In one region of phase space, with characteristic scales smaller than 1/m, the black hole threshold is dominated by the Choptuik solution and type II critical phenomena occur. In another it is dominated by metastable oscillating boson stars (whose mass is of order 1/m in geometric units) and type I critical phenomena occur. (For the real scalar field, the type I critical solution is an (unstable) oscillating boson star [186

] while for the complex scalar field it can be a static (unstable) boson star [120

].)

When the scalar field with a potential is coupled to electromagnetism, type II criticality is still controlled by a solution which asymptotically resembles the uncharged Choptuik spacetime, but type I criticality is now controlled by charged boson stars [176 ]. There are indications that subcritical type I evolutions lead to slow, large amplitude oscillations of stable boson stars [141 , 142 , 176 ] and not to dispersion to infinity, as had been conjectured in [120 ]. Another interesting extension is the study of the dynamics of a real scalar field with a symmetric double-well potential, in which the system displays type I criticality between the two possible vacua [128 ].