Holograghic Brownian motion in three dimensional G\"{o}del black hole

TL;DR

This paper investigates the holographic Brownian motion of a heavy quark in a three-dimensional G"{o}del black hole background using AdS/CFT, revealing new behaviors for certain parameter regimes and connecting to prior BTZ black hole results.

Contribution

It extends previous work on Brownian motion in black holes by analyzing the G"{o}del black hole case with $oldsymbol{ eq1}$, introducing a redefined angular velocity for string fluctuations.

Findings

Derived the time evolution of displacement squared in G"{o}del black hole background.

Showed the behavior of Brownian particles in non-relativistic limit.

Results reduce to known BTZ black hole case when $oldsymbol{ ightarrow1}$.

Abstract

By using the AdS/CFT correspondence and G\"{o}del black hole background, we study the dynamics of heavy quark under a rotating plasma. In that case we follow Atmaja (JHEP 1304, 021, (2013)) about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of $\alpha^{2}l^{2}\neq1$. This case, we must redefine the angular velocity of string fluctuation. We obtain the time evolution of displacement square that angular velocity and show that it behaves as a Brownian particle in non-relativistic limit. In this plasma, it seems that relating the Brownian motion with physical observables is rather a difficult work. But our results match with Atmaja work in the limit $\alpha^{2}l^{2}\rightarrow1$.