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Bulk viscosity and n-component fluids

Saga Säppi*

  • *Contact author: sappi@ieec.cat

Phys. Rev. D 114, 016009 – Published 9 July, 2026

DOI: https://doi.org/10.1103/3hqb-q7h6

Abstract

Understanding the hydrodynamics of out-of-equilibrium dense viscous fluids is of key importance to accurate descriptions of physical systems such as compact stars, particularly their mergers. We consider a near-equilibrium relativistic fluid with n independent and small chemical potentials restoring the system back toward equilibrium. By diagonalizing the evolution equation for the out-of-equilibrium chemical potentials, we construct an explicit evolution equation for the bulk scalar of the system in second-order hydrodynamics in terms of equilibrium quantities. We find expressions for the 2n transport quantities and show that, in the rest frame of the fluid, the system admits a Green’s function corresponding to an n-component fluid.

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References (22)

  1. B. P. Abbott et al. (SKA South Africa/MeerKAT Collaborations), Multi-messenger observations of a binary neutron star merger, Astrophys. J. Lett. 848, L12 (2017).
  2. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170817 observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  3. L. Baiotti and L. Rezzolla, Binary neutron star mergers: A review of Einstein’s richest laboratory, Rep. Prog. Phys. 80, 096901 (2017).
  4. M. G. Alford, L. Bovard, M. Hanauske, L. Rezzolla, and K. Schwenzer, Viscous dissipation and heat conduction in binary neutron-star mergers, Phys. Rev. Lett. 120, 041101 (2018).
  5. E. R. Most, A. Haber, S. P. Harris, Z. Zhang, M. G. Alford, and J. Noronha, Emergence of microphysical bulk viscosity in binary neutron star postmerger dynamics, Astrophys. J. Lett. 967, L14 (2024).
  6. M. G. Alford, S. Han, and K. Schwenzer, Signatures for quark matter from multi-messenger observations, J. Phys. G 46, 114001 (2019).
  7. M. Chabanov and L. Rezzolla, Impact of bulk viscosity on the postmerger gravitational-wave signal from merging neutron stars, Phys. Rev. Lett. 134, 071402 (2025).
  8. M. Chabanov and L. Rezzolla, Numerical modeling of bulk viscosity in neutron stars, Phys. Rev. D 111, 044074 (2025).
  9. J. Cruz Rojas, T. Gorda, C. Hoyos, N. Jokela, M. Järvinen, A. Kurkela, R. Paatelainen, S. Säppi, and A. Vuorinen, Estimate for the bulk viscosity of strongly coupled quark matter using perturbative QCD and holography, Phys. Rev. Lett. 133, 071901 (2024).
  10. J. L. Hernandez, C. Manuel, and L. Tolos, Damping of density oscillations from bulk viscosity in quark matter, Phys. Rev. D 109, 123022 (2024).
  11. O. P. Jyothilakshmi, P. E. S. Krishnan, P. Thakur, V. Sreekanth, and T. K. Jha, Hyperon bulk viscosity and r-modes of neutron stars, Mon. Not. R. Astron. Soc. 516, 3381 (2022).
  12. M. Alford, A. Harutyunyan, and A. Sedrakian, Bulk viscosity of relativistic NPE μ matter in neutron-star mergers, Particles 5, 361 (2022).
  13. M. Alford, A. Harutyunyan, and A. Sedrakian, Bulk viscosity of baryonic matter with trapped neutrinos, Phys. Rev. D 100, 103021 (2019).
  14. S. P. Harris, B. Fore, and S. Reddy, Bulk viscosity of nuclear matter with pions in the neutrino-trapped regime, Phys. Rev. C 111, 015802 (2025).
  15. J. L. Hernandez, C. Manuel, S. Säppi, and L. Tolos, Burgers equation for the bulk viscous pressure of quark matter, Phys. Rev. D 113, 014032 (2026).
  16. B. Carter, Covariant theory of conductivity in ideal fluid or solid media, Lect. Notes Math. 1385, 1 (1989).
  17. H. T. Banks, S. Hu, and Z. R. Kenz, A brief review of elasticity and viscoelasticity for solids, Adv. Appl. Math. Mech. 3, 1 (2011).
  18. S. Park and R. Schapery, Methods of interconversion between linear viscoelastic material functions. Part I—A numerical method based on Prony series, Int. J. Solids Struct. 36, 1653 (1999).
  19. R. Schapery and S. Park, Methods of interconversion between linear viscoelastic material functions. Part II—An approximate analytical method, Int. J. Solids Struct. 36, 1677 (1999).
  20. S. Park and Y. Kim, Fitting Prony-series viscoelastic models with power-law presmoothing, J. Mater. Civ. Eng. 13, 26 (2001).
  21. L. Gavassino, Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars, Classical Quantum Gravity 40, 165008 (2023).
  22. S.-H. Hou, Classroom note: A simple proof of the LeVerrier–Faddeev characteristic polynomial algorithm, SIAM Rev. 40, 706 (1998).

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