Relativistic Analogue of the Newtonian Fluid Energy Equation with Nucleosynthesis

TL;DR

This paper derives a relativistic fluid energy equation that explicitly includes nuclear energy generation, aligning with Newtonian models and improving the consistency of simulations involving nuclear reactions in relativistic contexts.

Contribution

It introduces a self-consistent relativistic energy equation explicitly incorporating nuclear energy generation, bridging Newtonian and relativistic fluid dynamics in nuclear astrophysics.

Findings

Derived a relativistic energy equation with explicit nuclear energy source term.

Showed the equation reduces to Newtonian form in the appropriate limit.

Provided a framework for more accurate relativistic nuclear fluid simulations.

Abstract

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 internal + 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.