  Nonlinear higher-spin equations in four dimensions admit a closed two-form
that defines a gauge-invariant global charge as an integral over a
two-dimensional cycle. In this paper we argue that this charge gives rise to
partitions depending on various lower- and higher-spin chemical potentials
identified with modules of topological fields in the theory. The vacuum
contribution to the partition is calculated to the first nontrivial order for a
solution to higher-spin equations that generalizes AdS4 Kerr black hole of
General Relativity. The resulting partition is non-zero being in parametric
agreement with the ADM-like behavior of a rotating source. The linear response
of chemical potentials to the partition function is also extracted. The
explicit unfolded form of 4d GR black holes is given. An explicit formula
relating asymptotic higher-spin charges expressed in terms of the generalized
higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is
obtained.
