The fate of Lorentz frame in the vicinity of black hole singularity

TL;DR

This paper investigates how quantum effects near black hole singularities challenge the existence of Lorentz frames, suggesting a fundamental limit to the applicability of current physical theories at Planck-scale distances.

Contribution

It introduces a novel analysis of tidal forces and quantum length scales to determine the finite region where Lorentz frames and classical theories break down near singularities.

Findings

Lorentz frames cease to exist at a finite radius from the singularity.

Classical and quantum theories are inapplicable within this critical radius.

Quantum corrections prevent the formation of a well-defined Lorentz frame near singularities.

Abstract

General Relativity is known to break down at singularities. However, it is expected that quantum corrections become important when the curvature is of the order of Planck scale avoiding the singularity. By calculating the effect of tidal forces on a freely falling inertial frame, and assuming the least possible size of the frame to be of the Planck length, we show that the Lorentz frames cease to exist at a finite distance from the singularity. Within that characteristic radius, one cannot apply General Relativity nor Quantum Field Theory as we know them today. Additionally we consider other quantum length scales and impose limits on the distances from the singularity at which those theories can conceivably be applied within a Lorentz frame.