Formulations of the 3+1 evolution equations in curvilinear coordinates

Understand

Following Brown, in this paper we give an overview of how to modify standard hyperbolic formulations of the 3+1 evolution equations of General Relativity in such a way that all auxiliary quantities are true tensors, thus allowing for these formulations to be used with curvilinear sets of coordinates such as spherical or cylindrical coordinates.

• After considering the general case for both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulations, we specialize to the case of spherical symmetry and also discuss the issue of regularity at the origin.
• Finally, we show some numerical examples of the modified BSSN formulation at work in spherical symmetry.