Numerical relativity in spherical coordinates : a new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit

Vassilios Mewes ... [et al.].

Serie: Trabajos publicados del IAR ; no. 1552

Resumen: We present SphericalNR, a new framework for the publicly availableEinstein Toolkit that numerically solves the Einstein field equationscoupled to the equations of general relativistic magnetohydrodynamic(GRMHD) in a 3 +1 split of spacetime in spherical coordinates withoutsymmetry assumptions. The spacetime evolution is performed usingreference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system withconstraint damping. We have developed a reference-metric version of theValencia formulation of GRMHD with a vector potential method,guaranteeing the absence of magnetic monopoles during the evolution. Inour framework, every dynamical field (both spacetime and matter) isevolved using its components in an orthonormal basis with respect to thespherical reference metric. Furthermore, all geometric information aboutthe spherical coordinate system is encoded in source terms appearing inthe evolution equations. This allows for the straightforward extensionof Cartesian high-resolution shock-capturing finite volume codes to usespherical coordinates with our framework. To this end, we have adaptedGRHydro, a Cartesian finite volume GRMHD code already available in theEinstein Toolkit, to use spherical coordinates. We present the fullevolution equations of the framework, as well as details of itsimplementation in the Einstein Toolkit. We validate SphericalNR bydemonstrating it passes a variety of challenging code tests in staticand dynamical spacetimes.