Logarithmic terms in entropy of Schwarzschild black holes in higher loops

Abstract: The Bekenstein-Hawking (BH) entropy is expected to be modified by certain correction terms in the quantum loop expansion. As is well known the logarithmic terms in the entropy of black holes appear as a one-loop addition to the classical BH entropy. In this note we study the further modifications of the logarithmic terms in the entropy of the Schwarzschild black holes due to higher quantum loops: up to three loops in a general renormalizable theory of gauge fields, scalars and fermions and two loops in quantum gravity. For a large class of field multiplets (including that of the Standard Model) that include graviton and for a certain range in the values of the couplings these modifications manifest themselves in cooling down the black holes at later stages of evaporation and, respectively, in increasing the life time of the black hole. If this picture persists to even higher loops, then the small black holes formed in the early stages of the cosmic evolution do not evaporate completely by now as is predicted in the standard picture. Instead, their long-lived (Planckian mass) remnants should present in abundance in today's Universe.