Magnetogravitational Instability of a Thermally Conducting Rotating Rivlin-Ericksen Fluid with Hall Current

Magnetogravitational instability of a thermally conducting, rotating Rivlin-Ericksen fluid with finite conductivity in the presence of Hall-current with a uniform vertical magnetic field has been investigated. A general dispersion relation has been derived through relevant linearized perturbation equations. The effects of Hall currents and rotation on the condition of instability of system is examined for both longitudinal and transverse modes of propagation and it is found that for longitudinal propagation; viscoelasticity has damping effect on the system and Jeans' criterion remains unaffected.The effects of rotation and magnetic field are not observed in the modified Jeans' condition of instability,whereas in the presence of thermal conductivity, the system is necessarily stable if Jeans' condition is not satisfied. The stability of the system is discussed using Routh-Hurwitz criterion. For transverse mode of propagation;the magnetic field and rotation stabilize the system. Jeans'criterion is also discussed for instability and stability of the system.