Maximum force conjecture in Kiselev, $4$D-EGB and Barrow corrected-entropy black holes

Abstract: The classical maximum force bound in the general relativity (GR) is defined between two black holes with touching horizons. We consider the maximum force conjecture for Kiselev solution that the black holes surrounded by quintessential matter, $w=-2/3$. We show that the maximum force bound is independent of black hole masses in this solution and we also indicate that when two black holes surrounded by static quintessence, the maximum force between them can approach to zero. In continue, we also study the maximum force bound for $4$D Einstein-Gauss-Bonnet ($4$D-EGB) black holes and we obtain that in this theory the maximum force bound exists and the force is bigger than the maximum force in GR. Finally, we consider the Barrow entropy in the framework of the entropic force theories and find that the maximum force only holds when the exponent of the corrected-entropy, namely $\Delta$, goes to zero and for other ranges of $\Delta$ it does not hold in which the mass dependence in the maximum force bound may cause the formation of naked singularities.