BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes

Understand

Brown has recently introduced a covariant formulation of the BSSN equations which is well suited for curvilinear coordinate systems.

• This is particularly desirable as many astrophysical phenomena are symmetric with respect to the rotation axis or are such that curvilinear coordinates adapt better to their geometry.
• However, the singularities associated with such coordinate systems are known to lead to numerical instabilities unless special care is taken (e.g., regularization at the origin).
• Cordero-Carrion will present a rigorous derivation of partially implicit Runge-Kutta methods in forthcoming papers, with the aim of treating numerically the stiff source terms in wave-like equations that may appear as a result of the choice of the coordinate system.