Is Bekenstein's conjecture true for charged black holes?

It is known that the thermal radiation from an uncharged, nonrotating black hole into a vacuum carries an entropy about 4/3 times the entropy lost by the hole. For a black hole placed in a radiation bath with a temperature infinitesimally close to that of the hole, the entropy of the radiation is equal to the hole's entropy loss. This previously known result is here extended to the case of a charged black hole, which gives further support to the statistical interpretation of black hole entropy.