Free hyperboloidal evolution in spherical symmetry

Abstract

We address the hyperboloidal initial value problem in the context of Numerical Relativity, motivated by its evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity, the location in spacetime where radiation is to be extracted. Our approach uses the BSSN and Z4 formulations and a time-independent conformal factor. The resulting system of PDEs includes formally diverging terms at null infinity. Here we discuss a regularized numerical scheme in spherical symmetry. A critical ingredient are the gauge conditions, which control the treatment of future null infinity. Stable numerical evolutions have been performed with regular and black hole initial data on a hyperboloidal slice. A sufficiently large scalar field perturbation will create a black hole, whose final stationary state is different from the trumpet initial data derived here.