The geometry of RN-AdS fluids

TL;DR

This paper explores the geometric structure of a fluid model that mimics RN-AdS black holes, analyzing scalar curvature, the Widom line, and geodesic behavior near critical points to deepen understanding of black hole thermodynamics.

Contribution

It establishes the parameter space geometry of RN-AdS fluids, linking it to black hole thermodynamics, and provides analytical and numerical insights into critical phenomena and geometric scaling.

Findings

Scalar curvature matches RN-AdS black hole in specific limit

Analytical construction of the Widom line for the fluid

Geodesic behavior exhibits scaling near critical point

Abstract

We establish the parameter space geometry of a fluid system characterized by two constants, whose equation of state mimics that of the RN-AdS black hole. We call this the RN-AdS fluid. We study the scalar curvature on the parameter space of this system, and show its equivalence with the RN-AdS black hole, in the limit of vanishing specific heat at constant volume. Further, an analytical construction of the Widom line is established. We also numerically study the behavior of geodesics on the parameter space of the fluid, and find a geometric scaling relation near its second order critical point.