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

TL;DR

This paper presents a covariant expression for the relative Lorentz factor in curved spacetime, demonstrating that energy conservation during particle decay in Kerr spacetime necessitates mass loss of the parent particle to produce kinetic energy in decay products.

Contribution

It introduces a new covariant formula for the relative Lorentz factor in curved spacetime and applies it to clarify energy conservation during particle decay in Kerr black hole environments.

Findings

Energy conservation in Kerr spacetime decay processes is verified analytically.

Mass loss of the parent particle is required for decay products to separate.

High-precision reconstructions confirm the theoretical conservation relations.

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.