Analytic approximate charged black hole solutions in Einstein–quartic gravity

In this work, we employ continued fraction expansions to derive analytical, approximate charged black hole solutions in Einstein–Maxwell–quartic gravity, a theory that introduces quartic curvature corrections to the Einstein–Hilbert action. To construct the full solution, we first obtain the metric function near the event horizon and at asymptotically large distances and then smoothly connect these regions using the continued fraction method. We further compute the associated thermodynamic quantities and verify the validity of the first law of black hole thermodynamics and the Smarr relation within this framework. We find that the thermodynamic analysis reveals van der Waals-type phase transitions between small and large black holes, with critical parameters that exhibit a universal ratio independent of the model parameters. Furthermore, the quasi-normal mode analysis indicates that the resulting spacetime is dynamically stable.