Quantum-mechanical corrections to the Schwarzschild black-hole metric

Motivated by quantum-mechanical corrections to the Newtonian potential, which can be translated into a h-correction to the g00 component of the Schwarzschild metric, we construct a quantum-mechanically corrected metric assuming -g00 = g^rr. We show how the Bekenstein blackhole entropy S receives its logarithmic contribution provided the quantum-mechanical corrections to the metric are negative. In this case the standard horizon at the Schwarzschild radius rS increases by small terms proportional to h and a remnant of the order of Planck mass emerges.