N-dimensional gravitational collapse with dark energy

We study the evolution of an N-dimensional anisotropic fluid with kinematic self-similarity of the second kind and find a class of solutions to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (p(r) =omega rho) and that the fluid moves along timelike geodesics. As in the four-dimensional case, the self-similarity requires omega = -1. The energy conditions and geometrical and physical properties of the solutions are studied. We find that, depending on the self-similar parameter alpha, they may represent black holes or naked singularities. We also study the presence of dark energy in some models, and find that their existence gives rise to some constraints on the dimensions of the space-times.