Effective Mass of Holographic Brownian Particle in Rotating Plasma

TL;DR

This paper investigates the effective mass of a Brownian particle modeled by a string in rotating black hole backgrounds, revealing it scales with the Lorentz factor cubed, extending previous results to more general rotating black holes.

Contribution

It introduces a new method to compute the effective mass of a Brownian particle in rotating black hole backgrounds and generalizes the result to asymptotically AdS_3 black holes.

Findings

Effective mass scales as γ^3 times the zero-temperature mass.

The method confirms previous results for co-rotating strings.

Generalization to asymptotically AdS_3 black holes.

Abstract

The dynamic of string fluctuation under rotating BTZ black hole is studied using the method of \cite{Son:2009vu}. We compare the result with previous computation in \cite{Atmaja:2012jg}, with a different method, for the case of co-rotating string. The result gives definite answer that the end of string identified as an external quark at the boundary behaves as Brownian particle with mass is given an effective mass $M_{eff}$ equal to the zero temperature mass of external quark $M_0$ times Lorentz factor $\gamma$ to the power three. We also extend the computation for general case of rotating black hole where the metric is asymptotically $AdS_3$ and the fluctuation is taken only along the co-rotating motion. It shows that the effective mass of the external quark is in general given by $\gamma^3 M_0$.