New look at the critical behavior near the threshold of black hole formation in the Russo-Susskind-Thorlacius model

The dependence of the critical exponent β on the shape of the incoming flux near the threshold of black hole formation is first studied in the context of the Russo-Susskind-Thorlacius (RST) model. In order to describe a generic incoming flux, two parameters (α,n) are first introduced. The critical exponent β is found to be 1/n, which is parameter dependent. And β=0.5 is not universal; it is just a special case for n=2. The apparent horizon and singularity curves for the generic parameter n are also evaluated in the scaling limit, which do not take the universal form. The singularity curve for n=1 even includes the parameter α. All of these indicate that critical phenomena perhaps do not exist in the RST model due to the linear nature of the RST equations which also results in no self-similar oscillations in the RST model.