Particle creation, clock variables, and relabelling symmetry in pull-back variational fluids

Abstract

Particle-number conservation is usually built into the pull-back variational formulation of relativistic fluids because the conservative Eulerian variation of the number current is compatible with flow-aligned relabellings only when \(\nabla_a n^a=0\). We revisit this obstruction when the matter-space density itself carries particle-creation information. The result is best organized by the fate of the flow-aligned relabelling. If creation is encoded by the proper-time functional of the deformed worldline, the endpoint variation of proper time cancels the timelike creation residual, so that the relabelling remains a current-level gauge symmetry even when \(Γ_N\neq0\). The price is a history term proportional to acceleration, which vanishes on geodesic flows, including homogeneous FLRW backgrounds. Local descriptions behave differently. With an independent scalar clock or interacting matter spaces, the Eulerian current variation generally retains a timelike residual proportional to \(Γ_Nu^a\). In the Andersson--Comer multi-fluid construction this residual is absorbed by the coupled force balance and represents inter-species conversion. In single-flow self-creation, where no partner matter-space force is available, the same residual becomes the physical scalar mode of the creation clock. A standard local scalar clock satisfying \(u^a\nabla_aΘ=1\) supplies, through its dynamics or constraint, the scalar equation replacing particle-number conservation; in dissipative systems it may be interpreted as entropic time. Clock choices that reproduce the same homogeneous FLRW creation history need not agree at linear order: the proper-time clock gives a creation-rate perturbation locked to the perturbed expansion, whereas a local scalar clock generically produces a gauge-invariant creation-rate mismatch, sourcing non-adiabatic creation pressure and modifying the effective sound speed.

20 pages, 1 figure, title changed