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arXiv · 2108.06135

Interaction Between AdS Black Hole Molecules

Suvankar Dutta·Gurmeet Singh Punia
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Abstract

We take a bottom-up approach to find the interaction potential between the $AdS$ black hole molecules under mean-field approximation. We start with the equation of state of dyonic $AdS$ black holes in fixed charge ensemble and use the method of classical cluster expansion to find the mean-field potential. We show that the Lennard-Jones (LJ) potential is a feasible choice to describe the equation of state. The LJ potential describes a two-body interaction. There exists a critical distance $r_0$ such that two interacting particles repel (attract) each other for $r < r_0$ ($r > r_0$). We compute the value of $r_0$ for dyonic $AdS$ black holes and compare the result obtained from the Ruppeiner scalar curvature. Our analysis shows how the electric (and magnetic) charge effects the interaction between black hole molecules.

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Suvankar Dutta, Gurmeet Singh Punia. 2021-12-15. Interaction Between AdS Black Hole Molecules. https://doi.org/10.1103/physrevd.104.126009

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