centra

 

Abstract: Gravitational wave radiation, our window for probing the strong field and dynamical regime of gravity, is unambiguously defined only at infinity, a region of spacetime difficult to reach from a numerical point of view. A convenient way of including infinity in numerical relativity simulations is by evolving along hyperboloidal slices: smooth spacelike slices that reach future null infinity - the location in spacetime where light rays arrive and thus where signals can be unambiguously extracted and global properties of spacetimes measured. The hyperboloidal initial value problem for the Einstein equations is addressed through conformal compactification methods, which we express in terms of unconstrained evolution schemes based on the BSSN and conformal Z4 formulations. The main difficulty of the implementation is that the resulting system of PDEs includes formally diverging terms at null infinity that require a special treatment and a careful choice of gauge conditions. In this first step in spherical symmetry, we present stable numerical evolutions of a massless scalar field coupled to the Einstein equations, including the collapse of a scalar field perturbation into a black hole and a scalar field perturbing a Schwarzschild black hole trumpet geometry. These successful results make this approach of the hyperboloidalinitial value problem a good candidate for more general numerical setups, like its implementation in a 3-dimensional code. The final goal of this work is to provide a far-field numerical framework based on the evolution on hyperboloidal slices that will effectively include null infinity in simulations of compact object mergers, hoping to reduce the systematic errors in current gravitational wave extraction and so provide more accurate waveforms.