  We consider unconstrained evolution schemes for the hyperboloidal initial
value problem in numerical relativity as a promising candidate for the
optimally efficient numerical treatment of radiating compact objects. Here,
spherical symmetry already poses nontrivial problems and constitutes an
important first step to regularize the resulting singular PDEs. We evolve the
Einstein equations in their generalized BSSN and Z4 formulations coupled to a
massless self-gravitating scalar field. Stable numerical evolutions are
achieved for black hole initial data, and critically rely on the construction
of appropriate gauge conditions.
