Quantum-mechanical corrections to the Schwarzschild black-hole metric

Motivated by quantum mechanical corrections to the Newtonian potential, which can be translated into an -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 black hole 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 and a remnant of the order of Planck mass emerges. We contrast these results with a positive correction to the metric which, apart from a corrected Schwarzschild horizon, leads to a new purely quantum mechanical horizon.