In superfluid dark matter, the charge tied to the chemical potential is not conserved, so the chemical potential is only an approximation valid on timescales much shorter than 10^8 years; the paper gives the correct prescription and a two-field alternative.
Gravitationally Bound Bose Condensates with Rotation
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abstract
We develop a self-consistent, Gravitoelectromagnetic (GEM) formulation of a slowly rotating, self-gravitating and dilute Bose-Einstein condensate (BEC), intended for astrophysical applications in the context of dark matter halos. GEM self-consistently incorporates the effects of frame dragging to lowest order in $v/c$ via the Gravitomagnetic field. BEC dark matter has attracted attention as an alternative to Cold dark matter (CDM) and Warm dark matter (WDM) for some time now. The BEC is described by the Gross-Pitaevskii-Poisson (GPP) equation with an arbitrary potential allowing for either attractive or repulsive interactions. Owing to the difficulty in obtaining exact solutions to the GEM equations of motion without drastic approximations, we employ the variational method to examine the conditions under which rotating condensates, stable against gravitational collapse, may form in models with attractive and repulsive quartic interactions. We also describe the approximate dynamics of an imploding and rotating condensate by employing a collective coordinate description in terms of the condensate radius.
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The role of the chemical potential in coupling superfluid dark matter to baryons
In superfluid dark matter, the charge tied to the chemical potential is not conserved, so the chemical potential is only an approximation valid on timescales much shorter than 10^8 years; the paper gives the correct prescription and a two-field alternative.