Multidomain spectral code for punctures without excision: The spherical case

Abstract

We present the first spectral method to evolve a single black hole treated as a puncture, therefore without singularity excision. We consider the Galerkin-Collocation method in single and multidomains to integrate the extended Baumgarte-Shapiro-Shibata-Nakamura formulation. In addition, we adopt the moving puncture approach but consider distinct Bona-Mass\'o slicing families instead of the standard $1+\mathrm{log}$ slicing condition. Further, we implement the maximal slicing version of the spectral code, where the lapse satisfies an elliptic-like equation.