Astronomical Institute, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
We point out the existence of a new type of growing transverse mode in the gravitational instability. This appears as a post-Newtonian effect to Newtonian dynamics. We demonstrate this existence by formulating the Lagrangian perturbation theory in the framework of the cosmological post-Newtonian approximation in general relativity. Such post-Newtonian order effects might produce characteristic appearances of large-scale structure formation, for example, through the observation of anisotropy of the cosmic microwave background radiation (CMB).