Article

# Magnetohydrodynamics in full general relativity: Formulation and tests

Physical review D: Particles and fields 07/2005; DOI: 10.1103/PhysRevD.72.044014

Source: arXiv

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**ABSTRACT:**We obtain the general forms for the current density and the vorticity from the integrability conditions of the basic equations which govern the stationary states of axisymmetric magnetized self-gravitating barotropic objects with meridional flows under the ideal magnetohydrodynamics (MHD) approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic fields act oppositely on the internal structures. The different actions of these two physical quantities, the meridional flows and the poloidal magnetic fields, could be clearly seen through stationary structures of the toroidal gaseous configurations around central point masses in the framework of Newtonian gravity because the effects of the two physical quantities can be seen in an amplified way for toroidal systems compared to those for spheroidal stars. The meridional flows make the structures more compact, i.e. the widths of toroids thinner, while the poloidal magnetic fields are apt to elongate the density contours in a certain direction depending on the situation. Therefore, the simultaneous presence of the internal flows and the magnetic fields would work as if there were no such different actions within and around the stationary gaseous objects such as axisymmetric magnetized toroids with internal motions around central compact objects under the ideal MHD approximation, although these two quantities might exist in real systems.Monthly Notices of the Royal Astronomical Society 05/2013; 431(2):1453-1469. · 5.52 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A flexible spectral code for the study of general relativistic magnetohydrodynamics is presented. Aiming at investigating the physics of slowly rotating magnetized compact stars, this new code makes use of various physically motivated approximations. Among them, the relativistic anelastic approximation is a key ingredient of the current version of the code. In this paper, we mainly outline the method, putting emphasis on algorithmic techniques that enable to benefit as much as possible from the non-dissipative character of spectral methods, showing also a potential astrophysical application and providing a few illustrative tests.Classical and Quantum Gravity 01/2007; 24(12). · 3.56 Impact Factor -
##### Article: General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

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**ABSTRACT:**We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This aims at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as in the evolution of magnetized neutron stars or in the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code extends the Eulerian conservative high-order (ECHO) scheme (Del Zanna et al. 2007, A&A, 473, 11) for GRMHD, here coupled to a novel solver of the Einstein equations in the extended conformally flat condition (XCFC). We solve the equations in the 3 + 1 formalism, assuming axisymmetry and adopting spherical coordinates for the conformal background metric. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and are solved, for each harmonic, by inverting band diagonal matrices. As a side product, we built and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.Astronomy and Astrophysics 01/2011; 528. · 5.08 Impact Factor

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