Binding Energy Across Classical Black Holes

A Horizon-Based Thermodynamic Approach

Abstract

We present analytic expressions for the dimensional quantity

B.E. = κMr₊,

which combines surface gravity κ, black hole mass M, and event-horizon radius r₊, across classical black-hole spacetimes: Kerr–Newman (rotating, charged), Kerr (rotating), Reissner–Nordstrom (charged), and Schwarzschild (neutral, non-rotating). This expression serves as a thermodynamic energy proxy, reflecting the interplay between horizon properties and gravitational binding in black holes. It recovers the classical result 1/2 Mc² for the Schwarzschild case and vanishes in extremal limits—consistent with the third law of black hole thermodynamics. We further discuss implications for gravitational energy extraction and astrophysical jet formation.