Numerical Relativity in Spherical Coordinates

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Numerical Relativity in Spherical Coordinates Working Group

Team: Lead: Manuela Campanelli (RIT)

  • Vassilios Mewes (RIT)
  • Yosef Zlochower (RIT)
  • Zach Etienne (WVU)
  • Ian Ruchlin (WVU)
  • Thomas Baumgarte (Bowdoin)


  • NSF 1550436 (Einstein Toolkit)
  • etc


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.

We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries.


  • Parity boundary conditions completed.
  • Implementation of BSSN equations in Spherical coordinates completed.
  • Interface to AHFinderDirect completed.
  • Interface to QuasiLocalMeasures completed.
  • Interface to TwoPunctures completed.
  • Radiation extraction code completed.


  • Submitted Paper "Numerical Relativity in Spherical Coordinates with the Einstein Toolkit", by Mewes, Zlochower, Campanelli, Ruchlin, Etienne, and Baumgarte [1]
  • Implementation of Hydro in Spherical Coordinates ... Begun.