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

Understand

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.