Equation of state for a classical gas of BPS black holes

A point particle treatment to the statistical mechanics of BPS black holes in Einstein-Maxwell-dilaton theory is developed. Because of the absence of the static potential, the canonical partition function for $N$ BPS black holes can be expressed by the volume of the moduli space for them. We estimate the equation of state for a classical gas of BPS black holes by Pad'e approximation and find that the result agrees with the one obtained by the mean-field approximation.