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00925njm 22002777a 4500 dc Ayuso, Ismael author Saez Gómez, Diego author 2020 Extremal cosmological black holes are analysed in the framework of the most general second order scalar-tensor theory, the so-called Horndeski gravity. Such extremal black holes are a particular case of Schwarzschild-De Sitter black holes that arises when the black hole horizon and the cosmological one coincide. Such metric is induced by a particular value of the effective cosmological constant and is known as Nariai spacetime. The existence of this type of solutions is studied when considering the Horndeski Lagrangian and its stability is analysed, where the so-called anti-evaporation regime is studied. Contrary to other frameworks, the radius of the horizon remains stable for some cases of the Horndeski Lagrangian when considering perturbations at linear order. Universe, 2020, Vol. 6, Nº.11, 210 2218-1997 https://uvadoc.uva.es/handle/10324/58800 10.3390/universe6110210 210 11 Universe 6 2218-1997 Gravitation Physics Classical and Quantum Gravitation, Relativity Theory Cosmology Black holes (Astronomy) Extremal cosmological black holes in Horndeski gravity and the anti-evaporation regime