Discreteness of Space from GUP in Strong Gravitational Fields

Abstract

A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale. It has also been shown that the GUP induces perturbative corrections to all quantum mechanical Hamiltonians, even at low energies, and thereby introduces Planck scale corrections to the Schrödinger equation and to the relativistic quantum mechanical equations. Some of these corrections give rise to potentially measurable effects in the low-energy laboratory. Another prediction of these corrections is that a measured length must be quantized, as seen by studying the solutions of the GUP modified Schrödinger, Klein-Gordon, and Dirac equations in a one, two, and three dimensional box. This result was subsequently extended to spacetimes with weak gravitational fields. In this work, we further extend this length quantization to spacetimes with strong gravitational fields and show that this result continues to hold, thereby showing that it is robust.

14 pages, accepted in Physics Letters B, published version with minor corrections

References in corpus (6)

• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• GUP parameter from quantum corrections to the Newtonian potential
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Lorentz-covariant deformed algebra with minimal length
• Reply to "Comment on 'Universality of Quantum Gravity Corrections' "

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• Investigating the shadows of new regular black holes with a Minkowski core: Effects of spherical accretion and core type differences
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Effects of underlying topology on quantum state discrimination
• GUP/BEB correspondence