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An analysis of MHD wave propagating in a gravitating and rotating mediumpermeated by non-uniform magnetic field has been done. It has been found thatthe Gradient of Magnetic Field when coupled with Rotation becomes capable togenerate few instabilities (Temporal or Spatial) leading to the damping oramplification of MHD waves. The Jean's criterion is not sufficient forstability always. Rather, the waves will suffer instability unless their wavelength (frequency) is less (greater) than certain critical values. Otherwise,those will smoothly propagate outward. Out of different scenarioes depending onthe direction of the magnetic field, its gradient, rotation and wavepropagation three important Special Cases have been discussed and differentstability criteria have been derived.  Finally, using the above theory we have obtained the stability/instabilitycriteria for the waves moving parallel and perpendicular to the galactic planein the Core and Periphery of the Central Region of Galaxy (C.R.G.) due to thecoupled action of Rotation and Non-Uniform Magnetic field. The possibility ofheating or occuring diffused condition inside the central region by MHD wavesor smooth propagation of these waves (under some restrictions) through theC.R.G. has been briefly discussed. The numerical values of the parameters ofthose waves for instabilities or smooth propagation have been estimatedroughly. One may find some clues for the formation of Halo and Spiral Arms.

Instabilities of MHD Waves Produced by Coupling of Rotation and Gradient  of Magnetic Field and its Possible Application in the Galactic Central Region