Numerical construction of hyperboloidal initial data using the parabolic-hyperbolic form of the constraints

Constructing hyperboloidal initial data free of logarithmic singularities at future null infinity is challenging. We construct hyperboloidal perturbed Kerr initial data by numerically integrating the parabolic-hyperbolic form of the constraints. We argue that the resulting initial data is sufficiently smooth at null infinity, extending the work of Beyer and Ritchie. We also determine the corresponding Bondi mass observing the limit of the Hawking mass.