  We consider the hyperboloidal initial value problem in numerical relativity,
motivated by the goal to evolve radiating compact objects such as black hole
binaries with a numerical grid that includes null infinity. Unconstrained
evolution schemes promise optimal efficiency, but are difficult to regularize
at null infinity, where the compactified Einstein equations are formally
singular. In this work we treat the spherically symmetry case, which already
poses nontrivial problems and constitutes an important first step. We have
carried out stable numerical evolutions with the generalized BSSN and Z4
equations coupled to a scalar field. The crucial ingredients have been to find
an appropriate evolution equation for the lapse function and to adapt
constraint damping terms to handle null infinity.
