Thermodynamics of nonlinearly charged anti-de Sitter black holes in four-dimensional critical gravity

In this paper we provide new examples of anti-de Sitter black holes with a planar base manifold in fourdimensional critical gravity by considering nonlinear electrodynamics as a matter source. We find a general solution characterized by the presence of only one integration constant where, for a suitable choice of coupling constants, we can show the existence of one or more horizons. Additionally, we compute its nonzero thermodynamical quantities through a variety of techniques, testing the validity of the first law of thermodynamics as well as a Smarr formula. Finally, we analyze the local thermodynamical stability of the solutions. To our knowledge, these charged configurations are the first example with critical gravity where their thermodynamical quantities are not zero.