  Non K\"ahler Calabi Yau theory is a newly developed subject and it arises
naturally in mathematical physics and generalized geometry. The relevant
geometrics are pluriclosed metrics which are critical points of the generalized
Einstein Hilbert action. In this work, we study the critical points of the
generalized Einstein Hilbert action and discuss the stability of critical
points which are defined as pluriclosed steady solitons. We proved that all
Bismut Hermitian Einstein manifolds are linearly stable which generalizes the
work from Tian, Zhu, Hall, Murphy and Koiso In addition, all Bismut flat
pluriclosed steady solitons with positive Ricci curvature are linearly strictly
stable.
