In UD theory, dark matter is the field UD, the D attribute in space. We derive the linearized Einstein equation from the UD action and show that the source term is the total energy-momentum tensor of all D attributes: Tµν = T(DD)µν + T(UD)µν. The UD field possesses pressure and anisotropic stress originating from its kinetic and potential terms. The anisotropic stress is quantified by the field gradients ∂iUD∂jUD, whose magnitude in a typical galactic halo is estimated from the selfconsistent UD density profile derived in this paper. The resulting quadrupole formula contains an additional contribution from UD. A stochastic gravitational wave background from dark matter dynamics is a necessary consequence of the theory, with an estimated peak amplitude ΩGW ∼ 10−12 at LISA frequencies, subject to an uncertainty of one to three orders of magnitude. The role of UD in gravitational wave physics is clarified: it acts as a source through its energy-momentum tensor, while its fluctuation enters the metric perturbation only at second order, ensuring that standard linear gravitational wave propagation remains unchanged in the far-field limit.
Dan Zhu (Wed,) studied this question.