Singularities and the Finale of Black Hole Evaporation

Abstract: In this essay we argue that once quantum gravitational effects change the classical geometry of a black hole and remove the curvature singularity, the black hole would not evaporate entirely but approach a remnant. In a modified Schwarzschild spacetime characterized by a finite Kretschmann scalar, a minimal mass of the black hole is naturally bounded by the existence of the horizon rather than introduced by hand. A thermodynamical analysis discloses that the temperature, heat capacity and the luminosity are vanishing naturally when the black hole mass approaches the minimal value. This phenomenon may be attributed to the existence of the minimal length in quantum gravity. It can also be understood heuristically by connecting the generalized uncertainty principle with the running of Newton's gravitational constant.