Topological Born–Infeld charged black holes in Einsteinian cubic gravity

In this paper, we study four-dimensional topological black hole solutions of Einsteinian cubic gravity in the presence of nonlinear Born–Infeld electrodynamics and a bare cosmological constant. First, we obtain the field equations which govern our solutions. Employing Abbott–Deser–Tekin and Gauss formulas, we present the expressions of conserved quantities, namely total mass and total charge of our topological black solutions. We disclose the conditions under which the model is unitary and perturbatively free of ghosts with asymptotically (A)dS and flat solutions. We find that, for vanishing bare cosmological constant, the model is unitary just for asymptotically flat solutions, which only allow horizons with spherical topology. We compute the temperature for these solutions and show that it always has a maximum value, which decreases as the values of charge, nonlinear coupling or cubic coupling grows. Next, we calculate the entropy and electric potential. We show that the first law of thermodynamics is satisfied for spherical asymptotically flat solutions. Finally, we peruse the effects of model parameters on thermal stability of these solutions in both canonical and grand canonical ensembles.