Minimal-length-triggered nonlinear electrodynamics corrections and singularity removal

Establish whether the existence of a minimal cut-off length \vartheta at Planck scales triggers nonlinear electrodynamics corrections and simultaneously removes the curvature singularity associated with the matter sector in the static, spherically symmetric electrically charged black hole configuration constructed from the action S = \int d^4x \sqrt{-g}[(R-2\Lambda)/(16\pi G^2) - \mathcal{L}(F_M)/(4\pi) + \mathcal{L}_m], with the anisotropic matter source and specified nonlinear electrodynamics Lagrangian \mathcal{L}(F_M) that recovers Maxwell electrodynamics at large distances.

Background

The paper proposes combining nonlinear electrodynamics (NED) with a minimal cut-off length \vartheta to address ultraviolet pathologies in charged black hole spacetimes. The authors adopt an ansatz of a static, spherically symmetric, electrically charged matter source and introduce a specific NED Lagrangian designed to regularize the electric field at short distances while recovering Maxwell theory at large scales.

Central to their construction is the conjecture that quantum fluctuations near the Planck scale necessitate modifications in both gravity and electrodynamics, with \vartheta acting as the trigger for NED corrections and the mechanism that removes curvature singularities in the matter sector. This conjecture underpins the regular black hole solution they derive and motivates further investigation into its foundational validity.