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In this paper we evolve magnetized and unmagnetized circumbinary accretiondisks around supermassive black hole binaries in the relativistic regime. Weuse a post-Newtonian expansion to construct an analytical spacetime anddetermine how the order of the post-Newtonian (PN) expansion affects thedynamics of the gas. We find very small differences in the late-time bulkdynamics of non-magnetized hydrodynamic evolutions between the two spacetimesdown to separations of approximately $40GM/c^2$ where $M$ is the total mass ofthe binary. For smaller separations, the differences due to PN-order becomecomparable to differences caused by using initial data further fromequilibrium. For magnetized gas, MHD stresses, which drives the accretiondynamics, tends to mask all higher order PN effects even at separations of$20GM/c^2$, leading to essentially the same observed electromagneticluminosity. This implies that our calculations of the EM signal may be robustdown to small binary separations. Our investigation is the first to demonstratehow the level of PN accuracy affects a circumbinary disk's evolution andinforms us of the range in separation within which to trust the PNapproximation for this kind of study. We also address the influence the initialconditions and binary separation have on simulation predictions.

Resolving the relative influence of strong field spacetime dynamics and MHD on circumbinary disk physics