Coarse-graining 1/2 BPS geometries of type IIB supergravity

Recently Lin, Lunin and Maldacena (LLM) (hep-th/0409174) explicitly mapped 1/2 BPS excitations of type IIB supergravity on AdS_5 x S^5 into free fermion configurations. We discuss thermal coarse-gaining of LLM geometries by explicitly mapping the corresponding equilibrium finite temperature fermion configuration into supergravity. Following Mathur conjecture, a prescription of this sort should generate a horizon in the geometry. We did not find a horizon in finite temperature equilibrium LLM geometry. This most likely is due to the fact that coarse-graining is performed only in a half-BPS sector of the full Hilbert space of type IIB supergravity. For temperatures much less than the AdS curvature scale the equilibrium background corresponding to nearly degenerate dual fermi-gas is found analytically.