Abstract
Linear and nonlinear propagation of self-gravitational perturbation mode in a super dense degenerate quantum plasma (containing heavy nuclei/element and degenerate electrons) has been investigated. The linear dispersion relation for this mode (associated with self-gravitational potential) has been derived and analyzed. On the other hand, the nonlinear propagation of this mode in such a degenerate quantum plasma system is examined by the reductive perturbation method, which is valid for a small but finite amplitude limit. It has been found that the nonlinear dynamics of small but finite amplitude self-gravitational perturbation mode in spherical geometry is governed by the modified Korteweg-de Vries (mKdV) equation with negative dispersion coefficient, and the numerical solutions of this mK-dV equation have been analyzed to identify the basic features of spherical self-gravitational potential structures that may form in such a super dense degenerate quantum plasma system. The implications of our results in astrophysical compact objects like neutron stars are briefly discussed.
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