  Building upon the work of Brendle, Marques and Neves on the construction of
counterexamples to Min-Oo's conjecture, we exhibit deformations of the de
Sitter-Schwarzschild space of dimension $n\geq 3$ satisfying the dominant
energy condition and agreeing with the standard metric along the event and
cosmological horizons, which remain totally geodesic. Our results actually hold
for generalized Kottler-de Sitter-Schwarzschild spaces whose cross sections are
compact rank one symmetric spaces and indicate that there exists no analogue of
the Penrose inequality in the case of positive cosmological constant. As an
application we construct solutions of Einstein field equations satisfying the
dominant energy condition and being asymptotic to (or agreeing with) the de
Sitter-Schwarzschild space-time both at the event horizon and at spatial
infinity.
