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

TL;DR

This paper investigates the maximum force conjecture across different black hole solutions, including Kiselev, 4D-EGB, and Barrow entropy models, revealing conditions under which the bound holds or breaks down.

Contribution

It extends the maximum force conjecture to black holes surrounded by quintessence, 4D-EGB black holes, and Barrow entropy, analyzing the conditions for the bound's validity.

Findings

Maximum force is mass-independent in Kiselev black holes.

Force can approach zero between black holes with quintessence.

Maximum force exceeds GR bounds in 4D-EGB 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.