The Coriolis field

Actually, in a gratifying acknowledgment of angular momentum conservation, they use two counter-rotating spinning wheels.

These terms are minus the acceleration $x¨0$ of the origin of the frame $S′$⁠, the centrifugal force per unit mass $−Ω×(Ω×r)$⁠, and the so-called Euler force per unit mass $−Ω̇×r$⁠.

This is best seen by considering the inverse change of frame, to which Eqs. (12) and (13) apply.

There is a huge literature about the analogies between electromagnetism and gravity in different regimes; see Refs. 22 and 23 and references therein.

The exact version of Eqs. (42)–(45) is obtained from Eqs. (90)–(91) and (93)–(94) of Ref. 22 taking the case of rigid frames (K_(ij) = θ = 0 therein) and a dust source, and restoring the c and G factors (c = G = 1 in the unit system of Ref. 22). They read $∇̃·G=−4πG(2γ2−1)ρ+H2/2+G2/c2, ∇̃×H=−(16πG/c2)j+(2/c2)G×H$⁠, $∇̃×G=−Ḣ, ∇̃·H=−G·H/c2$⁠, where $γ=(1−vmatter2/c2)−1/2$⁠. These equations yield Eqs. (21) exactly when c → ∞.