an:06827692
Zbl 1386.83031
Pugliese, D.; Valiente Kroon, J. A.
On the locally rotationally symmetric Einstein-Maxwell perfect fluid
EN
Gen. Relativ. Gravitation 48, No. 6, Paper No. 74, 28 p. (2016).
00356686
2016
j
83C15 83C22 83C55 53Z05 76W05
locally rotationally symmetric solutions; \(1+1+2\)-formalism; linear perturbations; stability; magnetohydrodynamics
Summary: We examine the stability of Einstein-Maxwell perfect fluid configurations with a privileged radial direction by means of a \(1+1+2\)-tetrad formalism. We use this formalism to cast in a quasilinear symmetric hyperbolic form the equations describing the evolution of the system. This hyperbolic reduction is used to discuss the stability of linear perturbations in some special cases. By restricting the analysis to isotropic fluid configurations, we assume a constant electrical conductivity coefficient for the fluid. As a result of this analysis we provide a complete classification and characterization of various stable and unstable configurations. We find, in particular, that in many cases the stability conditions are strongly determined by the constitutive equations and the electric conductivity. A threshold for the emergence of the instability appears in both contracting and expanding systems.