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Critical gravity is a quadratic curvature gravity in four dimensions which isghost-free around the AdS background. Constructing a Vaidya-type exactsolution, we show that the area of a black hole defined by a future outertrapping horizon can shrink by injecting a charged null fluid with positiveenergy density, so that a black hole is no more a one-way membrane even underthe null energy condition. In addition, the solution shows that the Wald-Kodamadynamical entropy of a black hole is negative and can decrease. Theseproperties expose the pathological aspects of critical gravity at thenon-perturbative level.

Decreasing entropy of dynamical black holes in critical gravity