Based on thermodynamics of positive and nega tiveenergy spectrum systems the complemental correspondence relations of the stabilizing criterion between the pcsitive and negative energy spectrum systems have been established. And then according as the Landau's theory, the theory for the exsitent condition of negative energy spectrum, and combing with the exact gravitational formula revised by general relativity has demonstrated that the high-density self-gravitationa l matter are the negative energy spectrum systems. Finally, on the basis of these complemental correspondence relations combing with the specific free energy of bigh-density self-gravitational systems, the stability of the negative energy spectrum systems have been analysed.