Speaker: Shalabh Gautam, International Center for Theoretical Sciences, Tata Institute of Fundamental Research

Title: Compactified Hyperboloidal Evolution in Numerical Relativity

Abstract: In the field of numerical relativity, a major challenge is to incorporate future null infinity into the computational domain using a well-posed formulation. Achieving this goal would not only allow us to accurately simulate any astrophysical system, such as binary black holes, and extract the resulting signal, like gravitational waves, at future null infinity, but it would also facilitate the study of various fundamental phenomena. One proposed solution is to use hyperboloidal slices. In this presentation, I will introduce an alternative approach to numerical relativity that leverages these slices in spherical symmetry. I will also discuss our ongoing efforts to establish a well-posed formulation of the Einstein Field Equations on these slices, and propose numerical schemes to ensure stability and convergence for linear hyperbolic systems over long durations. Additionally, I will present our method for constructing initial data corresponding to an asymptotically flat spacetime. A natural extension of our work will be to generalize these methods to the Einstein Field Equations with appropriate initial data in the full 3d.