Puncture black hole initial data in the conformal thin-sandwich formalism

We revisit the construction of puncture black hole initial data in the conformal thin-sandwich (CTS) decomposition of Einstein's constraint equations. It has been shown previously that this approach cannot yield quasiequilibrium wormhole data, which connect two asymptotically flat spatial infinities. This argument does not apply to trumpet data, which connect the spatial infinity in one universe with the future timelike infinity of another. As a numerical demonstration, we present results for a single boosted trumpet-puncture black hole, constructed in the original version of the CTS formalism.