Gravity waves in irrotational dust spacetimes are characterized by a nonzero magnetic Weyl tensor $H_{\mathrm{ab}}.$ In the linearized theory, the divergence of $H_{\mathrm{ab}}$ is set to zero. Recently Lesame, Ellis, and Dunsby [Phys. Rev. D 53, 738 (1996)] presented an argument to show that, in the exact nonlinear theory, $\mathrm{}\mathrm{div}H=0\mathrm{}$ forces $H_{\mathrm{ab}}=0\mathrm{}$, thus implying a linearization instability for gravity waves interacting with matter. However a sign error in the equations invalidates their conclusion. Bianchi type V spacetimes are shown to include examples with $\mathrm{}\mathrm{div}H=0\mathrm{}\ne H_{\mathrm{ab}}.$ An improved covariant formalism is used to show that in a generic irrotational dust spacetime the covariant constraint equations are preserved under evolution. It is shown elsewhere that $\mathrm{}\mathrm{div}H=0\mathrm{}$ does not generate further conditions.

• Received 22 April 1996

DOI:https://doi.org/10.1103/PhysRevD.55.463