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Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow.

Michal P Heller1,2,3, Alexandre Serantes2,4, Michał Spaliński2,5

  • 1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm, Germany.

Physical Review Letters
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Researchers explored relativistic hydrodynamics convergence properties using Israel-Stewart equations. They found factorially divergent gradient expansions in (1+1)D flows, except for specific symmetries, but divergence can be removed with a momentum cutoff.

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Area of Science:

  • Relativistic hydrodynamics
  • Nonlinear fluid dynamics
  • Theoretical physics

Background:

  • The gradient expansion is crucial for relativistic hydrodynamics but its convergence in nonlinear flows is poorly understood.
  • Previous studies were limited to simplified (0+1)-dimensional comoving flows like Bjorken flow.

Purpose of the Study:

  • To investigate the convergence properties of gradient expansions in relativistic hydrodynamics for general nonlinear flows.
  • To analyze fluids described by Israel-Stewart-type relaxation equations.

Main Methods:

  • Development of a simple method to analyze gradient expansion convergence.
  • Application of the method to (1+1)-dimensional flows.
  • Numerical simulations to provide evidence for theoretical predictions.

Main Results:

  • Numerical evidence for factorially divergent gradient expansions in (1+1)D relativistic hydrodynamics.
  • Demonstration that the only known convergent nonlinear hydrodynamic expansion relies on Bjorken flow symmetries.
  • Showed that factorial divergence can be mitigated using a momentum space cutoff.

Conclusions:

  • Gradient expansions in relativistic hydrodynamics are generally factorially divergent for nonlinear flows.
  • Bjorken flow symmetries are essential for convergence at the nonlinear level.
  • Momentum space cutoffs offer a method to control divergence, generalizing previous findings.