Many physicists agree that GR implies, under certain conditions, that gravity has a component, which if gravity is viewed as the analog of the electric force, is analogous to the magnetic force under a set of equations similar to Maxwell's equations. See e.g. http://arxiv.org/abs/gr-qc/0207065 Thus, a moving mass has additional effects not predicted by the simple Newtonian approximation. This gravitomagnetism effect is also know as "frame dragging." It also seems to imply that there are some clock effects to gravity even under this quasi-Maxwellian formulation. My question is, what are the most important implications of GR which are not captured by gravitomagnetism? One that seems obvious is that GR would apply to photons, while gravitomagnetism would seem not to, but it isn't intuitively obvious how much else the more sophisticated by classical gravitomagnetic expression fails to capture, and that one deviation, by itself, is a fairly trivial correction. The referenced article is: Matteo Luca Ruggiero and Angelo Tartaglia, "Gravitomagnetic Effects", To appear in Nuovo Cim. 117B (2002) 743-768 Abstract: This paper contains a review of the theory and practice of gravitomagnetism, with particular attention to the different and numerous proposals which have been put forward to experimentally or observationally verify its effects. The basics of the gravitoelectromagnetic form of the Einstein equations is expounded. Then the Lense-Thirring and clock effects are described, reviewing the essentials of the theory. Space based and Earth based experiments are listed. Other effects, such as the coupling of gravitomagnetism with spin, are described and orders of magnitude are considered to give an idea of the feasibility of actual experiments.