Some electrostatic implications of exponential corrections to black hole entropy

Quantum corrections to the Bekenstein–Hawking area law reveal profound insights into the nature of black hole entropy. The literature has established quantum corrections to the Bekenstein–Hawking area law: Exponential corrections of the form [Formula: see text] derived from horizon-confined quantum state enumeration. Building upon the entropic force framework of Verlinde, we demonstrate that the exponential modification to black hole entropy can provide a theoretical foundation for electrostatic phenomena. We develop a quantum-corrected formulation of Coulomb’s law and the Poisson equation for the scalar potential [Formula: see text], both of which integrate the exponential entropy correction derived from black hole physics. These findings strengthen the theoretical bridge between gravitational and electrostatic interactions, providing new evidence of the fundamental role of holographic principle in unifying these forces.