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

Abstract

The dependence of the critical exponent \ensuremath{\beta} 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 (\ensuremath{\alpha},n) are first introduced. The critical exponent \ensuremath{\beta} is found to be 1/n, which is parameter dependent. And \ensuremath{\beta}=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 \ensuremath{\alpha}. 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.