Physical implications of dominant energy condition behavior near the Planck scale

Characterize the physical implications of the observed behavior of the dominant energy condition for the matter sector in the regular charged black hole model, which is valid at large distances and near the Planck scale only when r \leq \sqrt{2}\vartheta, given the anisotropic stress-energy tensor built from the matter density \rho_m(r) = 3\vartheta^2 m/[8\pi (r^2 + \vartheta^2/2)^{5/2}] and the nonlinear electrodynamics contributions.

Background

The authors analyze standard energy conditions for their regular charged black hole sourced by an anisotropic matter distribution and a nonlinear electrodynamics sector. While the null and weak energy conditions are satisfied for each sector separately, the dominant energy condition exhibits nontrivial behavior in the matter sector near the Planck scale.

They note that, although the combined matter-plus-electric sector can satisfy the dominant energy condition under certain parameter constraints, the standalone matter sector’s behavior near \vartheta is not fully understood. They explicitly state that the physical implications of this result are unclear, motivating further investigation.