Black hole and fuzzy objects in the BFSS matrix model

Abstract

We conjecture fuzzy configurations of D0-branes in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model as microstates of the black hole. Fuzzy configurations of D0-branes consist of localized fuzzy objects in three spatial directions which are smeared into six internal directions. Since the solutions are time dependent, these are non-Bogomol'nyi-Prasad-Sommerfield (non-BPS) configurations and have internal energy compared with static case. Especially, we examine the smeared fuzzy sphere in the BFSS matrix model, which will correspond to the microstate of the charged black hole in four dimensions, and compare the effective potential in that background with the result obtained by the near horizon geometry of the black 0-brane. The qualitative features of two descriptions agree with each other; thus, we expect that the smeared fuzzy sphere corresponds to one of the microstates of the charged black hole. We also examine the smeared fuzzy cylinder which will correspond to the flat space time.