5.1.2 Acceleration Potential

In an irrotational spacetime, Eq. (46) becomes

$$P^{4}{}_{a}={\textstyle{\frac{1}{2}}}\mathrm{curl}(\dot{u}){}_{a}=0.$$ (75)

It introduces a scalar potential:

$$\dot{u}_{a}=\mathrm{D}_{a}\Phi,$$ (76)

where $\Phi$ is the acceleration potential. This scalar potential corresponds to the Newtonian potential. In the irrotational Newtonian model, the linearized acceleration is characterized as the acceleration potential.