Clustering of the collisionless particles in a gravitational field and rotation curve (Q674677)

T. Padmanabhan et al. discussed the effect of the gravitational field of a galaxy on a homogeneous collisionless cloud of dark matter by the linear approximation. In this work, the authors discuss the distribution of such collisionsless particles in an external field by solving the Boltzmann and Poisson equations in the second-order approximation. Besides the gravitational force being inversely proportional to the square of the distance, the result obtained also contains another force being inversely proportional to the distance. This result offers a reasonable explanation for the flatness of the rotation curves of the galaxies.