Equation of State of a Strongly Coupled Perfect Fluid with Spin from Holography

Abstract

We derive the equation of state of a strongly coupled relativistic perfect fluid with finite spin in $2+1$ dimensions using holography. The dual gravitational description is provided by a spinning black hole in $AdS_4$, whose Hawking temperature, angular velocity, and Bekenstein-Hawking entropy determine the thermodynamic properties of the boundary fluid. We obtain the equation of state and analyze its local thermodynamic stability, finding a critical rotation above which the fluid becomes thermodynamically unstable providing a bound for the rotation of a strongly coupled quark gluon plasma at temperature $T$ and angular velocity $ω$ given by $\frac{4πT}ω> 2.77239$. Remarkably, the same gravitational solution contains a second black hole associated with a second boundary. Although this black hole is non-spinning, its dual fluid rotates and possesses a distinct, ``exotic'' equation of state. Our results provide a holographic equation of state for strongly coupled matter with finite spin and establish a direct connection between black-hole rotation, intrinsic angular momentum, and the thermodynamic stability of relativistic fluids.