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GR: Fachverband Gravitation und Relativitätstheorie

GR 9: Numerische Relativitätstheorie I

GR 9.2: Vortrag

Mittwoch, 27. Februar 2013, 14:15–14:30, HS 6

Numerical Relativity in Spherical Polar Coordinates — •Pedro Montero — Max Planck Institute for Astrophysics

Development of numerical relativity codes in spherical polar coordinates has been hampered by the need to handle the coordinate singularities at the origin and on the axis, for example by careful regularization of the appropriate variables. Assuming spherical symmetry and adopting a covariant version of the BSSN equations, Montero and Cordero-Carrión recently demonstrated that such a regularization is not necessary when a partially implicit Runge-Kutta (PIRK) method is used for the time evolution of the gravitational fields. Here we report on an implementation of the BSSN equations in spherical polar coordinates without any symmetry assumptions. Using a PIRK method we obtain stable simulations in three spatial dimensions without the need to regularize the origin or the axis. We perform and discuss a number of tests to assess the stability, accuracy and convergence of the code, namely weak gravitational waves, ``hydro-without-hydro'' evolutions of spherical and rotating relativistic stars in equilibrium, and single black holes.