Static and radiating solutions of Lovelock gravity in the presence of a perfect fluid

We present a general solution of third order Lovelock gravity in the presence of a specific type II perfect fluid. This solution for linear equation of state, p=w(ρ−4B) contains all the known solutions of third order Lovelock gravity in the literature and some new static and radiating solutions for different values of w and B. Specially, we consider the properties of static and radiating solutions for w=0 and w=(n−2)−1 with B=0 and B≠0. These solutions are asymptotically flat for B=0, while they are asymptotically (anti-)de Sitter for B≠0. The new static solutions for these choices of B and w present black holes with one or two horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. The static solution with w=0 and vanishing geometrical mass (m=0) may present a black hole with two inner and outer horizons. This is a peculiar feature of the third order Lovelock gravity, which does not occur in lower order Lovelock gravity. We also, investigate the properties of radiating solutions for these values of B and w, and compare the singularity strengths of them with the known radiating solutions of third order Lovelock gravity.