  Trumpet geometries play an important role in numerical simulations of black
hole spacetimes, which are usually performed under the assumption of asymptotic
flatness. Our Universe is not asymptotically flat, however, which has motivated
numerical studies of black holes in asymptotically de Sitter spacetimes. We
derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter
spacetimes by first generalizing the static maximal trumpet slicing of the
Schwarzschild spacetime to static constant mean curvature trumpet slicings of
Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic
radial coordinate which results in a coordinate system analogous to McVittie
coordinates. At large distances from the black hole the resulting metric
asymptotes to a Friedmann-Lemaitre-Robertson-Walker metric with an
exponentially-expanding scale factor. While McVittie coordinates have another
asymptotically de Sitter end as the radial coordinate goes to zero, so that
they generalize the notion of a "wormhole" geometry, our new coordinates
approach a horizon-penetrating trumpet geometry in the same limit. Our
analytical expressions clarify the role of time-dependence, boundary conditions
and coordinate conditions for trumpet slices in a cosmological context, and
provide a useful test for black hole simulations in asymptotically de Sitter
spacetimes.
