Nariai-like black holes in light of scale-dependent gravity

In this work, we investigate for the first time Nariai-like black hole solutions in four dimensional space time with spherical symmetry in the context of scale-dependent gravity. In particular, we construct self-consistent solutions in such a way that the classical one that coming from Einstein theory) is also contained into our new results. We start by considering a truncated effective Einstein–Hilbert action with cosmological constant in which both the gravitational and the cosmological couplings are elevated to scale-dependent functions (instead of being coupling constants), taking advantage of the scale-dependent scenario, which is a concrete and simple approach strongly inspired by asymptotically safe gravity. We briefly discuss black hole thermodynamics and and compare it with its classical counterpart. The impact of non-Einsteinian features is encoded by the scale-dependent parameter, ϵ . A few comments regarding the topology of the solution and their impact are also mentioned.