Black hole polarization and new entropy bounds

Jacob D. Bekenstein∗ and Avraham E. Mayo† The Racah Institute of Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel (March 2, 1999) Zaslavskii has suggested how to tighten Bekenstein’s bound on entropy when the object is electrically charged. Recently Hod has provided a second tighter version of the bound applicable when the object is rotating. Here we derive Zaslavskii’s optimized bound by considering the accretion of an ordinary charged object by a black hole. The force originating from the polarization of the black hole by a nearby charge is central to the derivation of the bound from the generalized second law. We also conjecture an entropy bound for charged rotating objects, a synthesis of Zaslavskii’s and Hod’s. On the basis of the no hair principle for black holes, we show that this last bound cannot be tightened further in a generic way by knowledge of “global” conserved charges, e.g., baryon number, which may be borne by the object.