Quantum corrections to charged black holes need an extra consistency check

When gravity and electromagnetism are given scale-dependent couplings — a common approach to incorporating quantum corrections — the resulting black hole solutions must satisfy multiple consistency conditions simultaneously. Matching the equation-of-motion and action-level descriptions demands an additional quantum energy-momentum tensor and restricts the radial behavior of Newton's constant, while the electromagnetic coupling retains more freedom. A chemical-potential subtlety in the thermodynamics had been previously overlooked. The framework extends to cosmological settings, where quantum-induced coupling variations can smooth out anisotropies in the early universe.