ENTROPY OF NEAR-EXTREMAL BLACK P-BRANES

We carry out a thorough survey of entropy for a large class of p-brane s in various dimensions. We find that the Bekenstein-Hawking entropy m ay be given a simple world volume interpretation only for the non-dila tonic p-branes, those with the dilaton constant throughout spacetime. The entropy of extremal non-dilatonic p-branes is non-vanishing only f or solutions preserving 1/8 of the original supersymmetries. Upon toro idal compactification these reduce to dyonic black holes in 4 and 5 di mensions. For the self-dual string in 6 dimensions, which preserves 1/ 4 of the original supersymmetries, the near-extremal entropy is found to agree with a world sheet calculation, in support of the existing li terature. The remaining 3 interesting cases preserve 1/2 of the origin al supersymmetries. These are the self-dual 3-brane in 10 dimensions, and the 2- and 5-branes in 11 dimensions. For all of them the scaling of the near-extremal Bekenstein-Hawking entropy with the Hawking tempe rature is in agreement with a statistical description in terms of free massless fields on the world volume.