On the evolution equations for ideal magnetohydrodynamics in curved spacetime
arXiv:1112.1525 · doi:10.1007/s10714-012-1424-6
Abstract
We examine the problem of the construction of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Euler system. Our analysis is based on a 1+3 tetrad formalism which makes use of the components of the Weyl tensor as one of the unknowns. In order to ensure the symmetric hyperbolicity of the evolution equations implied by the Bianchi identity, we introduce a tensor of rank 3 corresponding to the covariant derivative of the Faraday tensor. Our analysis includes the case of a perfect fluid with infinite conductivity (ideal magnetohydrodynamics) as a particular subcase.
25 pages, no figures. New references added. Comments added in the Introduction. Accepted for publication in General Relativity and Gravitation
References in corpus (15)
- Cosmology with inhomogeneous magnetic fields
- WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
- Magnetospheres of Black Hole Systems in Force-Free Plasma
- Electromagnetic fields in curved spacetimes
- Relativistic magnetohydrodynamics in dynamical spacetimes: A new AMR implementation
- Magnetohydrodynamics in full general relativity: Formulation and tests
- Binary black holes' effects on electromagnetic fields
- Understanding possible electromagnetic counterparts to loud gravitational wave events: Binary black hole effects on electromagnetic fields
- Vacuum Electromagnetic Counterparts of Binary Black-Hole Mergers
- Cosmological models (Cargèse lectures 1998)
- General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes
- Motion of Isolated bodies
- Hyperbolicity of second-order in space systems of evolution equations
- Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies
- Uniqueness in MHD in divergence form: right nullvectors and well-posedness
Cited by in corpus (11)
- General classification of charged test particle circular orbits in Reissner--Nordström spacetime
- Ringed accretion disks: equilibrium configurations
- Ringed accretion disks: instabilities
- Ringed accretion disks: evolution of double toroidal configurations
- Proto-jets configurations in RADs orbiting a Kerr SMBH: symmetries and limiting surfaces
- RADs energetics and constraints on emerging tori collisions around super-massive Kerr Black Holes
- Relating Kerr SMBHs in Active Galactic Nuclei to RAD configurations
- Influence of toroidal magnetic field in multi-accreting tori
- On the evolution equations for a self-gravitating charged scalar field
- How the magnetic field behaves during the motion of a highly conducting fluid under its own gravity--A new theoretical, relativistic approach
- On the accreting tori sequences in Ringed Accretion Disks models. Polytropic equations of state and toroidal magnetic fields