MG14 - Talk detail

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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 "place" in spacetime where radiation is to be extracted. Our approach uses the BSSN and Z4 formulations, standard in current numerical codes, and also a time-independent compactification factor. The main difficulty is that the resulting system of PDEs includes formally diverging terms at null infinity that require a special treatment. This first step is restricted to spherical symmetry, although the regularization in the radial direction is expected to also apply to the full 3D case, at least to some extent. A critical ingredient are the gauge conditions, which rely on well-chosen source functions and damping terms. They also control the treatment of future null infinity. Stable numerical evolutions have been performed with regular and black hole initial data on a hyperboloidal slice. The signal of a massless scalar field has been successfully extracted at null infinity, and the simulations have been followed long enough to measure the scalar field's power-law decay tails.

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