⚛️ phenomenology

Shear induced cavitation in radially expanding, chemically equilibrating QGP

This study presents the first investigation of shear-induced cavitation in a chemically non-equilibrium, radially expanding Quark-Gluon Plasma, demonstrating that transverse expansion accelerates cavitation onset and establishing a critical shear viscosity threshold that constrains phenomenological models to ensure hydrodynamic validity.

Original authors: Lakshmi J. Naik, V. Sreekanth

Published 2026-09-22

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CC BY 4.0

Original authors: Lakshmi J. Naik, V. Sreekanth

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the most energetic collisions between atomic nuclei, scientists create a state of matter that existed only microseconds after the birth of the universe. This substance, known as the quark-gluon plasma, is a super-hot, super-dense soup where the fundamental building blocks of matter—quarks and gluons—float freely instead of being locked inside protons and neutrons. To understand how this primordial fireball behaves, physicists treat it like a fluid, using the mathematics of hydrodynamics to track how it expands and cools. A key property of any fluid is its thickness, or viscosity, which measures how much it resists flowing. In the case of this cosmic soup, the ratio of its viscosity to its entropy density is incredibly small, making it one of the most perfect fluids known to nature. However, if this fluid flows too quickly or expands too violently, the internal forces can become so extreme that the fluid's pressure drops below zero, causing it to tear apart into fragments. This phenomenon, known as cavitation, would signal a breakdown in the fluid model, suggesting that the standard equations used to describe the plasma are no longer valid.

A recent study by researchers Lakshmi J. Naik and V. Sreekanth investigates exactly when and how this tearing apart might happen in the quark-gluon plasma. They focused on a specific type of friction within the fluid called shear viscosity, which arises when different layers of the fluid slide past one another at different speeds. While previous studies had looked at how the plasma expands in a straight line, these researchers added a crucial new dimension: the plasma also expands outward in all directions, like a balloon inflating. They also accounted for the fact that the plasma is not perfectly balanced at the start; the number of quarks and gluons is not yet in equilibrium, a state known as chemical non-equilibrium. By combining these factors—radial expansion, chemical imbalance, and temperature-dependent viscosity—they simulated the evolution of the plasma to see if the internal pressure would ever drop low enough to cause it to break.

The researchers found that the addition of radial expansion is a game-changer. In a simpler model where the plasma only expands lengthwise, the fluid remains stable. But when the outward expansion is included, the shear forces become strong enough to drive the longitudinal pressure negative much earlier in the plasma's life. This cavitation does not happen everywhere at once. Instead, it begins at the very center of the fireball, where the temperature and density are highest, and then spreads outward toward the edges as time passes. This is a distinct pattern compared to other types of fluid instability, which often start at the edges and move inward. The study shows that this tearing apart occurs even while the plasma is still trying to reach a balanced state between its different particle types, meaning the chemical imbalance does not save the fluid from breaking.

A central goal of the paper was to determine the limits of the fluid model. The team calculated a critical threshold for the viscosity: if the fluid is thicker than this specific value, it will tear apart; if it is thinner, it will hold together. They discovered that the presence of radial expansion lowers this safety limit, meaning the plasma can tolerate less viscosity before it breaks. Interestingly, they found that the initial conditions matter greatly. If the plasma starts its life at a later time or with a specific imbalance of particles, it can withstand a higher viscosity without breaking. However, within the specific framework of this study, the viscosity values extracted from other experimental analyses fall below the critical threshold, suggesting that cavitation does not occur during the QGP evolution in these models. It is important to note that the obtained critical values should be interpreted as model-dependent thresholds rather than definitive quantitative bounds on the QGP transport coefficient, as a realistic equation of state and full numerical hydrodynamic evolution would be required for direct phenomenological constraints.

The work provides a necessary constraint on our understanding of the quark-gluon plasma. By showing that the fluid model holds up under realistic conditions of expansion and chemical imbalance within their framework, the researchers confirm that the standard equations are robust enough to describe the early universe's most extreme matter, provided the shear viscosity remains below the critical limit. They also highlight that the center of the fireball is the most vulnerable spot, where the fluid is most likely to fail first. While the study relies on simulations rather than direct measurement, the results offer a clear boundary for how "thick" this cosmic fluid can be before the laws of hydrodynamics cease to apply. This helps physicists refine their models and ensures that when they interpret data from particle colliders, they are not trying to force a fluid description onto a system that has already shattered.

Technical Summary: Shear Induced Cavitation in Radially Expanding, Chemically Equilibrating QGP

Problem Statement
The transport properties of the Quark-Gluon Plasma (QGP), particularly the shear viscosity to entropy density ratio ( $\eta/s$ ), are central to understanding collective flow in relativistic heavy-ion collisions. While causal second-order relativistic hydrodynamics successfully describes QGP evolution, this framework relies on the assumption that the system remains near local thermodynamic equilibrium. Strong viscous gradients can generate effective pressures that become negative, leading to cavitation (the fragmentation of the fluid) and a subsequent breakdown of the hydrodynamic description.

While cavitation driven by bulk viscosity near the phase transition temperature ( $T_c$ ) has been studied, cavitation induced by shear viscosity in an expanding medium remains less explored. Furthermore, existing studies often assume chemical equilibrium, whereas the QGP formed in early collision stages is known to be chemically undersaturated. Additionally, the role of robust transverse expansion dynamics in $\eta/s$ -induced cavitation has not been fully investigated. This paper addresses the interplay of shear viscosity, transverse expansion, and chemical non-equilibrium in determining the onset of cavitation.

Methodology
The authors model the QGP evolution using causal dissipative relativistic hydrodynamics within the Gubser geometry, which incorporates both longitudinal boost invariance and radial (transverse) expansion. The system is treated as a baryonless, massless parton gas with an ultrarelativistic equation of state ( $\varepsilon = 3P$ ).

Key methodological components include:

Chemical Non-Equilibrium: The chemical state is described using fugacities ( $\lambda_q, \lambda_g$ ) for quarks and gluons, which evolve from initial undersaturated values toward unity (equilibrium). The evolution is governed by master rate equations for dominant processes ( $gg \leftrightarrow ggg$ and $gg \leftrightarrow q\bar{q}$ ), coupled with hydrodynamic equations.
Shear Viscosity Prescriptions: The study employs several temperature-dependent $\eta/s(T)$ parameterizations, including phenomenological fits from Ref. [23], high-temperature QGP parameterizations (HH-HQ), and Bayesian analysis results (DUKE).
Hydrodynamic Framework: The authors solve the conservation of energy-momentum and particle number currents alongside the Israel-Stewart evolution equation for the shear stress tensor ( $\pi^{\mu\nu}$ ). The equations are solved in de Sitter coordinates (Gubser flow) and transformed back to Milne coordinates to analyze radial dependence.
Cavitation Criterion: Cavitation is identified when the effective longitudinal pressure ( $P_L = P + \pi$ ) becomes negative. The critical initial shear viscosity, $(\eta/s)_{\text{crit}}$ , is defined as the threshold below which cavitation does not occur throughout the evolution.

Key Results

Onset and Spatial Distribution: Shear-induced cavitation develops first at the center of the fireball ( $r=0$ ) at early proper times and subsequently extends radially outward. This contrasts with bulk-viscosity-driven cavitation, which typically initiates at larger radial distances before reaching the center.
Impact of Transverse Expansion: The inclusion of transverse expansion (Gubser flow) significantly accelerates the onset of cavitation compared to one-dimensional Bjorken expansion. In the Bjorken limit, cavitation was absent for certain parameterizations where it occurred in the Gubser case.
Critical Viscosity Thresholds: The study determines a critical initial shear viscosity, $(\eta/s)_{\text{crit}}$ , below which the hydrodynamic description remains valid. For the specific initial conditions used ( $T_0 = 0.83$ GeV, $\tau_0 = 0.23$ fm), $(\eta/s)_{\text{crit}}$ is found to be approximately 0.36 for a chemically equilibrating system and 0.35 for a fully equilibrated system.
Dependence on Initial Conditions:
- Temperature and Time: $(\eta/s)_{\text{crit}}$ increases with higher initial temperatures ( $T_0$ ) and later initial proper times ( $\tau_0$ ), implying that hotter or later-initialized systems can sustain larger shear viscosities without cavitation.
- Chemical Composition: Systems initialized with strong quark undersaturation (low $\lambda_q$ ) can sustain larger initial shear viscosities without cavitating, particularly at high $T_0$ .
- Comparison with Phenomenology: The phenomenologically extracted $\eta/s$ values from JETSCAPE Bayesian analyses lie below the calculated $(\eta/s)_{\text{crit}}$ within the authors' framework. This suggests that, under the current model assumptions, the extracted transport coefficients do not lead to cavitation.

Significance and Claims
The paper claims to present the first study of shear-induced cavitation that simultaneously incorporates transverse expansion and chemical non-equilibrium dynamics. The primary significance lies in establishing constraints on the shear viscosity of the QGP: for hydrodynamics to remain a valid description of heavy-ion collisions, the shear viscosity must remain below the critical threshold $(\eta/s)_{\text{crit}}$ to avoid negative longitudinal pressures.

The authors emphasize that while their results provide a constraint, the derived critical values are model-dependent thresholds based on conformal symmetry and Gubser geometry. They explicitly state that a realistic equation of state and full numerical hydrodynamic evolution would be necessary for direct quantitative phenomenological constraints. The work underscores that tracking the condition $P_L < 0$ is essential for successful hydrodynamic modeling of shear-viscous QGP evolution.

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