Entropy production by black holes

Abstract

HAWKING has shown¹ that black holes, treated quantum mechanically, emit black body radiation of temperature T = 10⁻⁷ (M_⊙/M_⊙) K, and hence evaporate—if isolated—on a time scale² of ∼ 10⁶⁶ (M/M_⊙)³ yr. Energy arguments^1,3,4 suggest that a black hole can be assigned the entropy where S_H ∼ 40(M/M_p)K is the entropy of a hydrogen cloud from which the black hole is assumed to have formed, M_p is the mass of the proton, and K is Boltzmann's constant. This implies that when a hydrogen cloud of mass 1M_⊙ collapses into a black hole, the entropy of the (uncollapsed) galaxy [∼ 10¹²S_H(M_⊙) and more] would increase by a factor ∼ 10⁶. In other words: something hardly observable, namely the collapse of one star, would increase the entropy of our cosmic neighbourhood by a large factor. We endeavour to resolve this apparent puzzle.