  Recent nonlinear completions of Fierz-Pauli theory for a massive spin-2 field
include nonlinear massive gravity and bimetric theories. The spectrum of
black-hole solutions in these theories is rich, and comprises the same vacuum
solutions of Einstein's gravity enlarged to include a cosmological constant. It
was recently shown that Schwarzschild (de Sitter) black holes in these theories
are generically unstable against spherical perturbations. Here we show that a
notable exception is partially massless gravity, where the mass of the graviton
is fixed in terms of the cosmological constant by \mu^2=2\Lambda/3 and a new
gauge invariance emerges. We find that general-relativity black holes are
stable in this limit. Remarkably, the spectrum of massive gravitational
perturbations is isospectral.
