A new concept to classically account for varying particle numbers in general relativity

A single classical massive point particle in general relativity is described by a timelike worldline, which plays a key role in the interpretation of spacetime curvature and the modern Hawking-Penrose definition of singularities. The very concept of such worldlines describing one single particle, however, is at severe odds with the key relativistic feature of energy-mass equivalence, since the latter allows for the annihilation of classical particles in favour of the creation of others. This report develops the kinematical set-up to remedy this problem by superseding the concept of a timelike worldline by the new concept of a history. The latter is one single object that captures all worldlines in a spacetime and also allows for the creation and annihilation of particles subject to energy-momentum conservation. This framework is then employed to generalize the free dynamics for massive particles to free dynamics for a history that describes a variable particle number and to discuss possible future applications in general relativity.