The formalism of energy conservation during particle decay in the Kerr spacetime

Abstract

We derive a compact, covariant expression for the relative Lorentz factor of two particles in curved spacetime and apply it to particle decay in Kerr spacetime. This allows us to show that energy conservation in the local center-of-mass frame requires the rest-mass loss of the parent particle to be converted into kinetic energy of the decay products. We verify this relation analytically and confirm it with high-precision reconstructions of three representative Penrose-process examples, for which both equivalent conservation formulas are satisfied to machine precision. These results clarify the local kinematics underlying energy extraction from rotating black holes and show that mass loss is not optional but is required for the decay products to separate.