Relativistic hydrodynamics with phase transition

F. Taghinavaz

doi:10.1140/epjc/s10052-024-13138-1

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 831
https://doi.org/10.1140/epjc/s10052-024-13138-1

Regular Article - Theoretical Physics

Relativistic hydrodynamics with phase transition

F. Taghinavaz^a

School of Particles and Accelerator, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

^a ftaghinavaz@ipm.ir

Received: 6 March 2024
Accepted: 19 July 2024
Published online: 19 August 2024

Abstract

Assessing the applicability of hydrodynamic expansions close to phase transition points is crucial from either theoretical or phenomenological points of view. We explore this within the gauge/gravity duality, using the Einstein–Klein–Gordon model, a bottom-up string theory construction. This model incorporates a parameter, $B_{4}$ $$B_4$$ , that simulates different types of phase transitions in the strongly coupled field theory existing at the boundary. We thoroughly examine the thermodynamics and dynamics of time-dependent, linearized perturbations in the spin-2, spin-1, and spin-0 sectors. Our findings suggest that ‘hydrodynamic series breakdown near transition points” is valid exclusively for second-order phase transitions, not for crossovers or first-order phase transitions. Additionally, we observe that the high-temperature and low-temperature limits of the radius of convergence for the hydrodynamic series ( $q_{c}^{2}$ $$q^2_c$$ ) are equal. We also discover that the relationship $(Max | q_{c}^{2} {|)}_{spin-2} < (Max | q_{c}^{2} {|)}_{spin-0} < (Max | q_{c}^{2} {|)}_{spin-1}$ $(\text {Max}|q^2_c|)_{\text {spin-2}}< (\text {Max}|q^2_c|)_{\text {spin-0}} < (\text {Max}|q^2_c|)_{\text {spin-1}}$ is consistent for different spin sectors, regardless of the phase transition type. At the chaos point, we observe the emergence of pole-skipping behavior for both gravity and scalar perturbations at $ω_{n} = - 2 π T n i$ $\omega _n = -2\pi T n i$ . Lastly, comparing the chaos momentum with $q_{c}^{2}$ $$q^2_c$$ , we find that $q_{ps}^{2} < q_{c}^{2}$ $q^2_{ps} < q^2_c$ , except for extremely high temperatures.

© The Author(s) 2024

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