Quantum corrections in general relativity explored through a GUP-inspired maximal acceleration analysis

TL;DR

This paper improves a maximum acceleration analysis by incorporating the GUP, revealing a finite quantum limit to gravitational acceleration in black holes and suggesting quantum corrections to general relativity occur at the Schwarzschild scale.

Contribution

It introduces a GUP-based approach to determine a finite maximum acceleration and applies it to black hole physics, challenging the notion that quantum effects only appear at the Planck scale.

Findings

Maximum acceleration is approximately 4c^2/l_P.

Quantum corrections prevent singularities in black holes.

Quantum effects become relevant at the Schwarzschild scale.

Abstract

A maximun acceleration analysis by Pati dating back to 1992 is here improved by replacing the traditional Heisenberg Uncertainty Principle (HUP) with the Generalized Uncertainty Principle (GUP), which predicts the existence of a minimum length in Nature. This new approach allows one to find a numerical value for the maximum acceleration existing in Nature for a physical particle that turns out to be a_{max}\simeq4\frac{c^{2}}{l_{P}}, that is, a function of two fundamental physical quantities such as the speed of light c and the Planck length l_{p}. An application of this result to black hole (BH) physics allows one to estimate a new quantum limit to general relativity. It is indeed shown that, for every real Schwarzschild BH, the maximum gravitational acceleration occurs, without becoming infinite, when the Schwarzschild radial coordinate reaches the gravitational radius. This means that quantum corrections to general relativity become necessary not at the Planck scale, as the majority of researchers in the field think, but at the Schwarzschild scale, in agreement with recent interesting results in the literature. In other words, the quantum nature of physics, which in this case manifests itself through the GUP, appears to prohibit the existence of real singularities, in this current case forbiddiing the gravitational acceleration of a Schwarzschild BH from becoming infinite.