The Magic of Translation: From Black Holes to Electricity express

Original: "The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective"
· Gokhan Alkac
arXiv:2605.14707v2 · 2026-05-14 · CC BY 4.0 · 1 min
Physicists have discovered that the laws of black holes can be rewritten in the language of electricity.

Physicists have learned to translate the equations of gravity into the language of electricity. This trick, double copy, works like a dictionary: it replaces the complex geometry of curved spacetime with simple electrical rules. When the method was applied to the simplest black holes, a coincidence emerged: the formula linking their mass, size, and entropy (a measure of disorder) exactly mirrors Gauss's law — the rule by which a charge creates a field around itself. Two different phenomena are described by the same mathematical pattern.

Most unexpected: if you place the same black hole in a special type of universe, it develops pressure and volume, like a gas piston. Gravity disguises itself as thermodynamics, hinting at a deep unity of all forces.

The double copy turns Einstein's equations into Maxwell's equations. Back in the 1970s, Hawking proved that black holes radiate heat. Now, that heat can be 'heard' in the language of electricity.

If a black hole with the mass of the Sun were to evaporate due to Hawking radiation, it would take $10^{67}$ years — billions of billions of times longer than the current age of the Universe.

In 'The Matrix,' reality is code. Here too: gravity and electricity might be different interfaces of a single hidden layer.

Scientists
Stephen HawkingJacob BekensteinFritz ZwickyKarl SchwarzschildSubrahmanyan ChandrasekharRainer Weiss
Concepts
kerr metric kerr black hole schwarzschild black hole schwarzschild metric Birkhoff's theorem zeroth law of thermodynamics scalar field area hawking area law wald entropy Schrödinger equation equation of state Einstein field equations flat space newtonian gravity solar mass Gauss's theorem charge to mass ratio classical gravity time reversal symmetry