The random walks of a Schwarzschild black hole

The purpose of this paper is to show that as a matter of principle, it is not appropriate to consider Schwarzschild black holes in thermal equilibrium with radiation because, even spinless and neutral holes undergo fluctuations of charge and angular momentum. Therefore, there will be a spread of these quantities around their zeromean values. We calculate these spreads for a black hole in thermal contact with charged scalar particles and show that angular momentum fluctuations are governed by the size of the cavity, larger cavities yielding larger angular momentum fluctuations. This behaviour is expected if black hole angular momentum fluctuations stem from the random absorption and emission of quanta with random angular momenta from the thermal bath. Furthermore, in the limit R/2M ≫ 1 charge fluctuations ∆Q/(ch̄) ∼ 1/(4π), that is to say, they become scale independent. This is expected if the underlying physics of these fluctuations is the random absorption and emission of charged quanta from the thermal bath. The independence of these fluctuations upon the elementary charge of the field is puzzling because it tells us that either the scale of the elementary charge is fixed by black hole physics to be α ∼ 1/4π (this gives an elementary charge which is only three times the charge of the electron), or the underlying physical process responsible these fluctuations is not known and remains to be cleared up. PACS: 04.70Dy, 04.62.+v On leave from University of Campinas e.mail [email protected]