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Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints

In this paper, we continue our investigations of Rácz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which we were able to resolve by introducing a certain modification of Rácz's parabolic-hyperbolic formulation. The primary focus of the present paper here is the asymptotically hyperboloidal setting. We provide evidence through a mixture of numerical and analytical methods that the asymptotics of the solutions of Rácz's parabolic-hyperbolic formulation is stable, and, in particular, no modifications are necessary to obtain solutions that are asymptotically hyperboloidal.