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

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.

14 pages, published in Physics Letters B

References in corpus (15)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• On Gravity and the Uncertainty Principle
• GUP parameter from quantum corrections to the Newtonian potential
• Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
• Relativistic Generalized Uncertainty Principle
• The generalized and extended uncertainty principles and their implications on the Jeans mass
• Black holes as Gravitational Atoms
• Schrödinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse
• Universality of minimal length
• Minimum length (scale) in Quantum Field Theory, Generalized Uncertainty Principle and the non-renormalisability of gravity
• Constraining the generalized uncertainty principle with neutron interferometry
• What happens at the horizon?
• Quantum oscillations in the black hole horizon