Multi-horizon and Critical Behavior in Gravitational Collapse of   Massless Scalar
  This paper studies the whole process of gravitational collapse and accretion of a massless scalar field in asymptotically flat spacetime. Two kinds of initial configurations are considered. One is the initial data without black hole, the other contains a black hole. Under suitable initial conditions, we find that multi-horizon will appear, which means that the initial black hole formed by gravitational collapse or existing at the beginning will instantly expand and suddenly grow, rather than grows gradually in the accretion process. A new type of critical behavior is found around the instant expansion. The numerical computation shows that the critical exponents are universal. 
Zhoujian Cao, Rong-Gen Cai, Run-Qiu Yang
gr-qc hep-th physics.comp-ph