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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We present a new numerical implementation of the general-relativistic
resistive magnetohydrodynamics (MHD) equations within the Whisky code. The
numerical method adopted exploits the properties of Implicit-Explicit
Runge-Kutta numerical schemes to treat the stiff terms that appear in the
equations for small electrical conductivities. Using tests in one, two, and
three dimensions, we show that our implementation is robust and recovers the
ideal-MHD limit in regimes of very high conductivity. Moreover, the results
illustrate that the code is capable of describing physical setups in all ranges
of conductivities. In addition to tests in flat spacetime, we report
simulations of magnetized nonrotating relativistic stars, both in the Cowling
approximation and in dynamical spacetimes. Finally, because of its
astrophysical relevance and because it provides a severe testbed for
general-relativistic codes with dynamical electromagnetic fields, we study the
collapse of a nonrotating star to a black hole. We show that also in this case
our results are in very good agreement with the perturbative studies of the
dynamics of electromagnetic fields in a Schwarzschild background and provide an
accurate estimate of the electromagnetic efficiency of this process.
