Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. A relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian $\text{internal}+\text{kinetic energy}$ in the appropriate limit—emerges naturally and self-consistently from the difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass $m$, when $m$ is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.

Figure 1

A common but problematic correspondence between Newtonian and relativistic fluid dynamics.

Figure 2

A conceptually sound Newtonian limit of relativistic fluid dynamics.