In recent years the equations of relativistic first-order viscous
hydrodynamics, that is, the relativistic version of Navier-Stokes, have been
shown to be well posed and causal under appropriate field redefinitions, also
known as hydrodynamic frames. We perform real-time evolutions of these
equations for a conformal fluid and explore, quantitatively, the consequences
of using different causal frames for different sets of initial data. By
defining specific criteria, we make precise and provide evidence for the
statement that the arbitrarily chosen frame does not affect the physics up to
first order, as long as the system is in the effective field theory regime.
Motivated by the physics of the quark-gluon plasma created in heavy-ion
collisions we also explore systems which are marginally in the effective field
theory regime, finding that even under these circumstances the first order
physics is robust under field redefinitions.
Recent studies have shown that the equations of relativistic first-order viscous hydrodynamics, similar to the Navier-Stokes equations, are well posed and causal when appropriate field redefinitions (referred to as hydrodynamic frames) are applied. In this article, we conduct real-time evolutions of these equations for a conformal fluid and investigate the implications of using different causal frames with various initial data sets. By establishing specific criteria, we provide evidence that the choice of frame does not significantly impact the physics at first order, as long as the system remains in the effective field theory regime.
This research is particularly motivated by the behavior of the quark-gluon plasma generated in heavy-ion collisions. We also analyze systems that are on the edge of the effective field theory regime and observe that even under these conditions, the first-order physics remains robust when subjected to field redefinitions.
Future Roadmap
To better understand the potential challenges and opportunities on the horizon in this field, it is important to consider several key aspects:
1. Further Investigation of Causal Frames
While this study establishes that different causal frames have minimal impact on the first-order physics, it would be valuable to conduct more extensive research to confirm these findings. This could involve exploring different fluid systems and studying additional criteria that may be relevant in determining the effects of causal frames. These investigations would contribute to a deeper understanding of the fundamental nature of relativistic first-order viscous hydrodynamics.
2. The Impact of Higher-Order Effects
The current research focuses specifically on first-order physics within the effective field theory regime. To fully comprehend the implications of causal frames, it is crucial to investigate whether higher-order effects come into play as the system transitions out of this regime. Understanding these effects will provide a more comprehensive understanding of the entire physics landscape for relativistic viscous hydrodynamics.
3. Experimental Confirmation
Experimental validation is an essential step in any scientific development. Conducting experiments, such as further heavy-ion collision studies, to compare with theoretical predictions based on different causal frames would solidify the conclusions drawn from this research. The collaboration between theoretical physicists and experimentalists is crucial in advancing our knowledge of relativistic first-order viscous hydrodynamics.
4. Applications in Other Fields
The insights gained from this research have the potential to be applied beyond the study of quark-gluon plasma and heavy-ion collisions. Exploring other areas of physics, such as astrophysics or condensed matter physics, may reveal analogous systems where relativistic viscous hydrodynamics plays a significant role. Investigating these applications will broaden the scope of the field and potentially lead to unexpected discoveries.
Conclusion
The research presented in this study highlights that, up to first order, the choice of causal frame has minimal impact on the physics of relativistic viscous hydrodynamics within the effective field theory regime. It also demonstrates the resilience of first-order physics under field redefinitions in both conformal fluid and marginally effective field theory systems. Moving forward, further investigation, consideration of higher-order effects, experimental validation, and application in other fields will continue to shape our understanding and utilization of relativistic first-order viscous hydrodynamics.