A note on the entropy of charged multi - black - holes

Majumdar--Papapetrou multi--black-hole solutions of the Einstein--Maxwell equations are considered in four and higher dimensions. The Euclidean action with boundary conditions appropriate to the canonical ensemble is shown to lead to zero entropy.Comment: LaTeX, 8 page

Black hole state counting in loop quantum gravity

The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity, one counting all allowed spin network labels j,m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation.Comment: 5 page

Reply to comment by Zaslavskii on extremal black hole action

It is shown that Zaslavskii's misunderstanding of our published proof of the irrelevance of all extremal black hole configurations (whether with equal charge and mass or not) rests on his refusal to see the essential difference between the correct inequality governing extremal and non-extremal actions and his incorrect version.Comment: 1 page, REVTeX, adapted from reply in PRL 80, 3413 (1998

Absence of log correction in entropy of large black holes

Earlier calculations of black hole entropy in loop quantum gravity led to a dominant term proportional to the area, but there was a correction involving the logarithm of the area, the Chern-Simons level being assumed to be large. We find that the calculations yield an entropy proportional to the area eigenvalue with no such correction if the Chern-Simons level is finite, so that the area eigenvalue can be relatively large.Comment: 8 page