Energy,fluidity, and Superconductivity of black holes in the Schwarzschild metric: Extension of membrane paradigm

This work presents an analytical extension to Thorne’s membrane paradigm to describe the electrodynamic, dissipative, and reactive properties of the event horizon in the Schwarzschild metric. By introducing a thought experiment based on a quantized Watt balance at the boundary of gravitational collapse, mass, surface gravity, and the Planck length are coupled to directly deduce the emergence of a fundamental quantum impedance within the horizon fluid. Upon integrating the Hawking radiation frequency and Joule’s law, the dynamic response of the membrane is formally mapped onto an RLC resonant circuit under an ideal critically damped condition with a strictly unitary quality factor. The exact analytical expressions for the effective inductance and capacitance are determined, revealing a symmetric equipartition of electrodynamic energy which, when coupled with Einstein’s gravitational constant, clean-cancels to yield the pure gravitational length of the space-time geometry. Finally, through the sub-microscopic geometric discretization provided by Regge calculus at Planck scales, a bridge is established with the granular geometry of the horizon, deriving an expression for the quantum resistance that converges identically into the pure von Klitzing constant at the fundamental quantum limit. These findings suggest an intrinsic and universal superconducting behavior governed strictly by the topology of the horizon.