Perturbative no-hair property of form fields for higher dimensional static black holes

In this paper we examine the static perturbation of p-form field strengths around higher dimensional Schwarzschild spacetimes. As a result, we can see that the static perturbations do not exist when p≥3. This result supports the no-hair properties of p-form fields. However, this does not exclude the presence of the black objects having nonspherical topology.