Black hole thermodynamics rewritten as a simple electrostatics law

Using the Kerr-Schild double copy — a map that translates static black hole solutions in general relativity into electric field configurations in flat spacetime — the Smarr formula, which relates a black hole's mass to its other thermodynamic quantities, reduces exactly to Gauss's law for the corresponding electromagnetic single copy. Extending this to anti-de Sitter spacetimes, the pressure-volume term in extended black hole thermodynamics emerges naturally from subtracting a gauge-theoretic background. The result suggests that some black hole thermodynamic identities may be shadows of simpler flat-spacetime electrostatics.