  We develop a new perturbation method to study the dynamics of massive tensor
fields on extremal and near-extremal static black hole spacetimes in arbitrary
dimensions. On such backgrounds, one can classify the components of massive
tensor fields into the tensor, vector, and scalar-type components. For the
tensor-type components, which arise only in higher dimensions, the massive
tensor field equation reduces to a single master equation, whereas the vector
and scalar-type components remain coupled. We consider the near-horizon
expansion of both the geometry and the field variables with respect to the
near-horizon scaling parameter. By doing so, we reduce, at each order of the
expansion, the equations of motion for the vector and scalar-type components to
a set of five mutually decoupled wave equations with source terms consisting
only of the lower-order variables. Thus, together with the tensor-type master
equation, we obtain the set of mutually decoupled equations at each order of
the expansion that govern all dynamical degrees of freedom of the massive
tensor field on the extremal and near-extremal static black hole background.
