Investigating the domain of validity of the Gubser solution to the Boltzmann equation

Heinz, Ulrich; Martinez, Mauricio

doi:10.1016/j.nuclphysa.2015.08.009

Investigating the domain of validity of the Gubser solution to the Boltzmann equation

Journal Article · Tue Sep 01 00:00:00 EDT 2015 · Nuclear Physics. A

DOI:https://doi.org/10.1016/j.nuclphysa.2015.08.009· OSTI ID:1604528

^[1]; Martinez, Mauricio ^[2]

The Ohio State Univ., Columbus, OH (United States); The Ohio State University
The Ohio State Univ., Columbus, OH (United States)

Here, we study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric transverse and boost-invariant longitudinal expansion. We show, for arbitrary values of the shear viscosity to entropy density ratio, that the distribution function can become negative in certain kinematic regions of the available phase space depending on the boundary conditions. For thermal equilibrium initial conditions, we determine numerically the physical boundary in phase space where the distribution function is always positive definite. The requirement of positivity of this particular exact solution restricts its domain of validity, and it imposes physical constraints on its applicability.

Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: SC0004104; SC0004286

OSTI ID:: 1604528

Alternate ID(s):: OSTI ID: 1347041
OSTI ID: 22569351

Journal Information:: Nuclear Physics. A, Journal Name: Nuclear Physics. A Journal Issue: C Vol. 943; ISSN 0375-9474

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (12)

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Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio Physical Review D, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevD.90.125026	journal	December 2014
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Analytic solutions of the relativistic Boltzmann equation Hatta, Yoshitaka; Martinez, Mauricio; Xiao, Bo-Wen Physical Review D, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevD.91.085024	journal	April 2015
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New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit Denicol, Gabriel S.; Heinz, Ulrich; Martinez, Mauricio Physical Review Letters, Vol. 113, Issue 20 https://doi.org/10.1103/PhysRevLett.113.202301	journal	November 2014

Cited By (5)

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime Bazow, D.; Denicol, G. S.; Heinz, U. Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/physrevd.94.125006	journal	December 2016
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M. Physical Review D, Vol. 97, Issue 4 https://doi.org/10.1103/physrevd.97.044041	journal	February 2018
Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow Behtash, Alireza; Kamata, Syo; Martinez, Mauricio Physical Review D, Vol. 99, Issue 11 https://doi.org/10.1103/physrevd.99.116012	journal	June 2019
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime Bazow, D.; Denicol, G. S.; Heinz, U. arXiv https://doi.org/10.48550/arxiv.1607.05245	text	January 2016
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M. arXiv https://doi.org/10.48550/arxiv.1711.01745	text	January 2017

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
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