Skip to main content

Advertisement

Log in

Dominant energy condition and dissipative fluids in general relativity

  • Research
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Existing literature implements the Dominant Energy Condition for dissipative fluids in general relativity. It is pointed out that this condition fails to forbid superluminal flows, which is what it is ultimately supposed to do. Tilted perfect fluids, which formally have the stress-energy tensor of imperfect fluids, are discussed for comparison.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data Availability

There are no data associated with this work because of its theoretical and mathematical nature.

Notes

  1. We use the notation of Ref. [13], in which the metric has signature \({-}{+}{+}{+}\) and units are used in which the speed of light c and Newton’s constant G are unity.

  2. At the time of writing, a cumulative citation count in Google Scholar returns 157 entries.

References

  1. Rezzolla, L., Zanotti, O.: Relativistic Hydrodynamics. Oxford University Press, Oxford (2013)

    Book  MATH  Google Scholar 

  2. Andersson, N., Comer, G.L.: Relativistic fluid dynamics: physics for many different scales. Living Rev. Rel. 24(1), 3 (2021). https://doi.org/10.1007/s41114-021-00031-6

    Article  MATH  Google Scholar 

  3. Andersson, N.: Gravitational waves from instabilities in relativistic stars. Class. Quantum Grav. 20, R105 (2003). https://doi.org/10.1088/0264-9381/20/7/201

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Maartens, R.: “Causal thermodynamics in relativity,” [arXiv:astro-ph/9609119 [astro-ph]]

  5. Hiscock, W.A., Lindblom, L.: On transient relativistic thermodynamics and kinetic theory. II. Phys. Lett. A 131, 509 (1988)

    Article  ADS  Google Scholar 

  6. Eckart, C.: The thermodynamics of irreversible processes. 3. Relativistic theory of the simple fluid. Phys. Rev. 58, 919–924 (1940). https://doi.org/10.1103/PhysRev.58.919

    Article  ADS  MATH  Google Scholar 

  7. Müller, I.: Zum Paradox der Wärmeleitungstheorie. Z. Phys. 198, 329 (1967)

    Article  ADS  MATH  Google Scholar 

  8. Stewart, J.M.: On transient relativistic thermodynamics and kinetic theory. Proc. R. Soc. Lond. Ser. A 357, 59 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  9. Israel, W., Stewart, J.M.: Transient relativistic thermodynamics and kinetic theory. Ann. Phys. 118, 341–372 (1979). https://doi.org/10.1016/0003-4916(79)90130-1

    Article  ADS  MathSciNet  Google Scholar 

  10. Israel, W., Stewart, J.M.: On transient relativistic thermodynamics and kinetic theory. II. Proc. R. Soc. Lond. Ser. A 365, 43–52 (1979). https://doi.org/10.1098/rspa.1979.0005

    Article  ADS  MathSciNet  Google Scholar 

  11. Carter, B.: Convective variational approach to relativistic thermodynamics of dissipative fluids. Proc. R. Soc. Lond. Ser. A 433, 45 (1991). https://doi.org/10.1098/rspa.1991.0034

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Müller, I., Ruggeri, T.: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998)

    Book  MATH  Google Scholar 

  13. Wald, R.M.: General Relativity. Chicago University Press, Chicago (1984)

    Book  MATH  Google Scholar 

  14. Carroll, S.M.: Spacetime and Geometry: An Introduction to General Relativity. Addison-Wesley, San Francisco (2004)

    MATH  Google Scholar 

  15. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1972)

    MATH  Google Scholar 

  16. Borde, A.: Geodesic focusing, energy conditions and singularities. Class. Quantum Grav. 4, 343 (1987). https://doi.org/10.1088/0264-9381/4/2/015

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Bekenstein, J.D.: Positiveness of Mass and the Strong Energy Condition. Int. J. Theor. Phys. 13, 317–321 (1975). https://doi.org/10.1007/BF01808371

    Article  Google Scholar 

  18. Barcelo, C., Visser, M.: Twilight for the energy conditions? Int. J. Mod. Phys. D 11, 1553–1560 (2002). https://doi.org/10.1142/S0218271802002888

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Martin-Moruno, P., Visser, M.: Classical and semi-classical energy conditions. Fundam. Theor. Phys. 189, 193–213 (2017). https://doi.org/10.1007/978-3-319-55182-1_9

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Kolassis, C.A., Santos, N.O., Tsoubelis, D.: Energy conditions for an imperfect fluid. Class. Quantum Grav. 5, 1329–1338 (1988). https://doi.org/10.1088/0264-9381/5/10/011

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Pimentel, O.M., González, G.A., Lora-Clavijo, F.D.: The energy-momentum tensor for a dissipative fluid in general relativity. Gen. Rel. Grav. 48(10), 124 (2016). https://doi.org/10.1007/s10714-016-2121-7

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Setiawan, A.M., Sulaksono, A.: Anisotropic neutron stars and perfect fluid’s energy conditions. Eur. Phys. J. C 79(9), 755 (2019). https://doi.org/10.1140/epjc/s10052-019-7265-7

    Article  ADS  Google Scholar 

  23. Ellis, G.F.R., Maartens, R., MacCallum, M.A.H.: Relativistic Cosmology. Cambridge University Press, Cambridge (2012)

    Book  MATH  Google Scholar 

  24. Tsumura, K., Kunihiro, T.: Uniqueness of Landau-Lifshitz energy frame in relativistic dissipative hydrodynamics. Phys. Rev. E 87(5), 053008 (2013). https://doi.org/10.1103/PhysRevE.87.053008

    Article  ADS  Google Scholar 

  25. Maartens, R., Gebbie, T., Ellis, G.F.R.: Covariant cosmic microwave background anisotropies. 2. Nonlinear dynamics. Phys. Rev. D 59, 083506 (1999). https://doi.org/10.1103/PhysRevD.59.083506

    Article  ADS  Google Scholar 

  26. Clarkson, C.A., Coley, A.A., O’Neill, E.S.D., Sussman, R.A., Barrett, R.K.: Inhomogeneous cosmologies, the Copernican principle and the cosmic microwave background: More on the EGS theorem. Gen. Rel. Grav. 35, 969–990 (2003). https://doi.org/10.1023/A:1024094215852

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Clarkson, C., Maartens, R.: Inhomogeneity and the foundations of concordance cosmology. Class. Quantum Grav. 27, 124008 (2010). https://doi.org/10.1088/0264-9381/27/12/124008

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported, in part, by the Natural Sciences and Engineering Research Council of Canada (Grant 2016-03803 to V.F.).

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study conception and design.

Corresponding author

Correspondence to Valerio Faraoni.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Faraoni, V., Mokkedem, E.M.Z.R. Dominant energy condition and dissipative fluids in general relativity. Gen Relativ Gravit 55, 56 (2023). https://doi.org/10.1007/s10714-023-03110-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-023-03110-x

Keywords

Navigation