Quantum Mechanical Corrections to the Schwarzschild Black Hole Metric

TL;DR

This paper investigates quantum corrections to the Schwarzschild black hole metric, revealing how these modifications affect the horizon size, entropy, and the emergence of quantum horizons, with implications for black hole remnants.

Contribution

It introduces a quantum mechanically corrected Schwarzschild metric based on $ abla$-corrections and analyzes their effects on black hole entropy and horizon structure.

Findings

Logarithmic correction to black hole entropy due to quantum effects

Increase in Schwarzschild horizon size by quantum corrections

Emergence of a new quantum horizon under positive corrections

Abstract

Motivated by quantum mechanical corrections to the Newtonian potential, which can be translated into an $\hbar$-correction to the $g_{00}$ component of the Schwarzschild metric, we construct a quantum mechanically corrected metric assuming $-g_{00}=g^{rr}$. 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 $r_S$ increases by small terms proportional to $\hbar$ 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.