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

Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c