Mass and charge fluctuations and black hole entropy

The effects of thermal fluctuations of the mass (horizon area) and electric charge, on the entropy of nonrotating charged macroscopic black holes, are analyzed using a grand canonical ensemble. Restricting to Gaussian fluctuations around equilibrium, and assuming a power-law type of relation between the black hole mass, charge and horizon area, characterized by two real positive indices, the grand canonical entropy is shown to acquire a logarithmic correction with a positive coefficient proportional to the sum of the indices. However, the root mean squared fluctuations of mass and charge relative to the mean values of these quantities turn out to be independent of the details of the assumed mass-area relation. We also comment on possible cancellation between log (area) corrections arising due to fixed area quantum spacetime fluctuations and that due to thermal fluctuations of the area and other quantities.