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Lovelock theory provides a tractable model of higher-curvature gravity inwhich several questions can be studied analytically. This is the reason why, inthe last years, this theory has become the favorite arena to study the effectsof higher-curvature terms in the context of AdS/CFT correspondence. Lovelocktheory also admits extensions that permit to accommodate matter coupled togravity in a non-minimal way. In this setup, problems such as the backreactionof matter on the black hole geometry can also be solved exactly. In this paper,we study the thermodynamics of black holes in theories of gravity of this type,which include both higher-curvature terms, U(1) gauge fields, and conformalcouplings with matter fields in D dimensions. These charged black holesolutions exhibit a backreacting scalar field configuration that is regulareverywhere outside and on the horizon, and may exist both in asymptoticallyflat and asymptotically Anti-de Sitter (AdS) spaces. We work out explicitly theboundary action for this theory, which renders the variational problemwell-posed and suffices to regularize the Euclidean action in AdS. We alsodiscuss several interrelated properties of the theory, such as its dualitysymmetry under field redefinition and how it acts on black holes andgravitational wave solutions.

Black hole thermodynamics, conformal couplings, and R^2 terms