The Magic of Double Copy: From Black Hole Geometry to the Laws of Electricity express

Physicists have mastered an elegant mathematical trick that lets them translate gravitational equations into the language of electricity. This method — double copy — works like a kind of dictionary: it replaces the complex geometry of curved spacetime, described by high-dimensional tensor fields, with the simpler rules of electromagnetism, where vector fields operate. When this approach was applied to the simplest black holes — those that don't rotate and have no electric charge — a striking coincidence emerged: the formula linking their mass, size, and entropy (a measure of internal disorder, or the amount of hidden information) mathematically exactly mirrors Gauss's law — the fundamental rule that an electric charge generates a field around itself, and the flux of that field through a closed surface is proportional to the enclosed charge. In other words, two seemingly completely different physical phenomena are described by the same mathematical structure.

The double copy turns the complex nonlinear equations of Einstein's gravitational field into the linear equations of Maxwell's electromagnetism, making them accessible to analysis with familiar methods. Back in the 1970s, Hawking, applying quantum field theory near the event horizon, proved that black holes aren't so black after all — they emit heat, known as Hawking radiation. Now, thanks to the double copy, this thermal radiation can be "heard" in the electric language — translated into terms of electromagnetic waves propagating from accelerated charges.