We update the method of the Holmberg & Flynn (2000) study, including an updated model of the Milky Way's interstellar gas, radial velocities, an updated reddening map, and a careful statistical analysis, to bound the allowed surface density and scale height of a dark disk. We pay careful attention to the self-consistency of the model, including the gravitational influence of the dark disk on other disk components, and to the net velocity of the tracer stars. We find that the data set exhibits a non-zero bulk velocity in the vertical direction as well as a displacement from the expected location at the Galactic midplane. If not properly accounted for, these features would bias the bound toward low dark disk mass. We therefore perform our analysis two ways. In the first, traditional method, we subtract the mean velocity and displacement from the tracers' phase space distributions. In the second method, we perform a non-equilibrium version of the HF method to derive a bound on the dark disk parameters for an oscillating tracer distribution. Despite updates in the mass model and reddening map, the traditional method results remain consistent with those of HF2000. The second, non-equilibrium technique, however, allows a surface density as large as 14 M ⊙ pc −2 (and as small as 0 M ⊙ pc −2 ), demonstrating much weaker constraints. For both techniques, the bound on surface density is weaker for larger scale height. In future analyses of Gaia data, it will be important to verify whether the tracer populations are in equilibrium.

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We introduce a potentially powerful method for constraining or discovering a thin dark matter disk in the Milky Way. The method relies on the relationship between the midplane densities and scale heights of interstellar gas being determined by the gravitational potential, which is sensitive to the presence of a dark disk. We show how to use the interstellar gas parameters to set a bound on a dark disk and discuss the constraints suggested by the current data. However, current measurements for these parameters are discordant, with the uncertainty in the constraint being dominated by the molecular hydrogen midplane density measurement, as well as by the atomic hydrogen velocity dispersion measurement. Magnetic fields and cosmic ray pressure, which are expected to play a role, are uncertain as well. The current models and data are inadequate to determine the disk's existence, but, taken at face value, may favor its existence depending on the gas parameters used.

We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. We comment on the implications of these results towards understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon.

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