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In this thesis, we approached the applications of the John sector of theHorndeski gravity in the scenarios of black brane, braneworld and cosmology.Specially, we study AdS/CFT correspondence in the context of the Horndeskigravity to evaluate the viscosity/entropy density ratio, as a function of thefixed exponent and parameters of theory. In the braneworld, we address theissue of finding braneworld solutions in a five-dimensional Horndeski gravityand discuss gravity localization. Finally, in the cosmological scenario wefinding solutions by using first-order formalism in the Horndeski gravity thatconstrains the superpotential and implies that no free choice of scalarpotential is allowed. The scalar field equation of state reflects well thecosmological scenario at the present time and allows us to conclude that it cansimulate the dark energy in the Horndeski gravity.

Aplica\c{c}\~oes do Setor John da Gravidade de Horndeski nos Cen\'arios  de Brana Negra e Rela\c{c}\~ao de viscosidade/entropia, Mundo Brana e  Cosmologia (In Portuguese)