C. Gundlach et Jm. Martingarcia, CHARGE SCALING AND UNIVERSALITY IN CRITICAL COLLAPSE, Physical review. D. Particles and fields, 54(12), 1996, pp. 7353-7360
Consider any one-parameter family of initial data such that data with
a parameter value p>p form black holes, and data with p<p* do not. As
p-->p from above (''critical collapse''), the black hole mass scales
as M similar to(p-p)(gamma), where the critical exponent gamma is th
e same for all such families of initial data. So far critical collapse
has been investigated only for initial data with zero charge and zero
angular momentum. Here, we allow for U(1) charge. In scalar electrody
namics coupled to gravity, with action R+\(partial derivative+iqA)phi\
(2)+F-2, we consider initial data with spherical symmetry and a nonvan
ishing charge. From dimensional analysis and a previous calculation of
Lyapunov exponents, we predict that in critical collapse the black ho
le mass scales as M similar to(p-p)(gamma), and the black hole charge
as Q similar to(p-p)(delta), with gamma=0.374+/-0.001 (as for the re
al scalar field) and delta=0.883+/-0.007. We conjecture that, where th
ere is no mass gap, this behavior generalizes to other charged matter
models, with delta greater than or equal to 2 gamma. We suggest the ex
istence of universality classes with respect to parameters such as q.