On the Hagedorn transition and collective dynamics of D0-branes

Banks, Fischler, Klebanov and Susskind have proposed a model for black hole thermodynamics based on the principle that the entropy is of order the number of particles at the phase transition point in a Boltzmann gas of D0-branes. We show that the deviations from Boltzmann scaling found in d < 6 noncompact spatial dimensions have a simple explanation in the analysis of self-gravitating random walks due to Horowitz and Polchinski. In the special case of d = 4 we find evidence for the onset of a phase transition in the Boltzmann gas analogous to the well-known Hagedorn transition in a gas of free strings. Out result relies on an estimate of the asymptotic density of states in a dilute gas of D0-branes. (C) 1998 Published by Elsevier Science B.V. All rights reserved.