Numerical relativity in spherical coordinates with the Einstein Toolkit

Understand

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates.

• While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes and accretion disks.
• While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically.
• This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities.