Abstract
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.
Highlights
The solutions in the context of Einsteinian cubic gravity (ECG) have been explored from different points of view
We studied four-dimensional topological Born–Infeld (BI) charged black hole solutions in the context of Einsteinian cubic gravity (ECG) in the presence of a bare cosmological constant
Topological black hole solutions are known to be dual to some thermal states in the holographic settings, with quite different thermodynamical features depending on the specific topology
Summary
The solutions in the context of ECG have been explored from different points of view. In [7], the static and spherically symmetric generalizations of four-dimensional linearly charged and uncharged black hole solutions in ECG have been constructed and their thermodynamics has been studied. The most general theory of gravity to cubic order in curvature called Generalized Quasi-Topological Gravity (GQTG) whose static spherically symmetric vacuum solutions are fully described by a single field equation has been constructed in [8]. In this theory, the ECG as well as Lovelock and quasi-topological gravities have been recovered in four dimensions as special cases.
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