Skip to main content
SpringerLink
Log in

Nöther Conserved Quantities and Entropy in General Relativity

  • Conference paper
Recent Developments in General Relativity, Genoa 2000

  • 216 Accesses

Abstract

In the framework of classical field theories, the notions of conserved quantities and entropy for stationary solutions of covariant theories of gravitation, e. g. of Einstein field equations of General Relativity, are discussed. Nöther theorem is used to provide the correct definition of (covariantly) conserved quantities such as mass and angular momentum. The variation of entropy is then defined as a macroscopical quantity which satisfies a Clausiuslike first principle of thermodynamics. Finally, a proposal for the entropy of non-stationary solutions is discussed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Misner, W., Thome, S., Wheeler, J.A. (1970): Gravitation. W.H. Freeman and Co, San Francisco

    Google Scholar 

  2. Penrose, R. (1982): Proc. R. Soc. London A, 381, 53

    Article  MathSciNet  ADS  Google Scholar 

  3. Hawking, S.W. (1975): Commun. Math. Phys. 43, 199

    Article  MathSciNet  ADS  Google Scholar 

  4. Iyer, V., Wald, R. (1994): Phys. Rev. D 50, 846

    Article  MathSciNet  ADS  Google Scholar 

  5. Fatibene, L., Ferraris, M., Francaviglia, M., Raiteri, M. (1999): Annals of Phys. 275, 27; hep-th/9810039

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Brown, J.D., York, J.W. (1993): Phys. Rev. D 47, 1420

    Article  MathSciNet  ADS  Google Scholar 

  7. Carter, B. (1979): In Black Holes, ed. by S.W. Hawking, W. Israel, Cambridge University Press, Cambridge

    Google Scholar 

  8. Hawking, S.V., Ellis, G.F.R. (1973): The large scale structure of spacetime. Cambridge University Press, Cambridge

    Book  Google Scholar 

  9. Frolov, V.P., Fursaev, D.V.: Thermal Fields, Entropy, and Black Holes. hep-th/9802010

    Google Scholar 

  10. Frolov, D.V.: Black holes entropy, and physics at Planckian scales. hep-th/9510156v3

    Google Scholar 

  11. Brown, J.D., York, J.W. (1993): Phys. Rev. D 47, 1407

    Article  MathSciNet  ADS  Google Scholar 

  12. Fatibene, L., Ferraris, M., Francaviglia, M., Raiteri, M.: Noether charges, Brown York quasi local energy and related topics. gr-qc/0003019, J. Math. Phys., in press

    Google Scholar 

  13. Fatibene, L., Ferraris, M., Francaviglia, M., Raiteri, M.: Entropy in General Relativity, in Proceedings for the conference in honour of De Ritis, in press

    Google Scholar 

  14. Brown, J.D., York, J.W: gr-qc9506085

    Google Scholar 

  15. Ferraris, M., Francaviglia, M. (1991): In Mechanics, Analysis and Geometry: 200 Years after Lagrange, ed. by M. Francaviglia, Elsevier

    Google Scholar 

  16. Gotay, M.J., Isenber, J., Marsden, J.E., Montgomery, R.: Momentum maps and classical relativistc fields. The Lagrangian and Hamiltonian structure of classical field theories with constrains; hep-th/9801019

    Google Scholar 

  17. Giachetta, G., Sardanashvily, G.: Stress energy momentum tensor in Lagrangian field theory. Part I: Superpotentials. E-print: gr-qc@xxx. lanl. gov. gr-qc/9510061

    Google Scholar 

  18. Trautman, A. (1962): Gravitation: an introduction to current research. Ed. by L. Witten Whiley, New York, pp. 168–198

    Google Scholar 

  19. Trautman, A. (1967): Commun. Math. Phys. 6, 248

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Ferraris, M., Francaviglia, M., Sinicco, I.: Il Nuovo Cimento, Vol. 107B, N. 11

    Google Scholar 

  21. Fatibene, L., Ferraris, M., Francaviglia, M. (1997): J. Math. Phys. 38,(8), 3953–3967

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Kolar, I., Michor, P.W, Slovak, J. (1993): Natural operations in differential geometry. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  23. Ferraris, M.: In proceedings of the conference on Differential Geometry and its applications, Part 2, Geometrical methods in Physics, ed. by D. Krupka, Brno, pp. 61–91

    Google Scholar 

  24. Katz, J. (1985): Class. Quantum Grav. 2, 423

    Article  ADS  Google Scholar 

  25. Iyer, V, Wald, R.: gr-qc 9503052

    Google Scholar 

  26. Regge, T., Teitelboim, C. (1974): Ann. Phys. 88, 286

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Fatibene, L., Francaviglia, M. (2002): Natural and Gauge Natural Formalism for Classical Field Theories. A Geometric Perspective including Spinors and Gauge Theories, in press

    Google Scholar 

  28. Fatibene, L. (1999): Gauge-natural formalism for classical field theories. Ph.D. Thesis, University of Turin

    Google Scholar 

  29. Francaviglia, M., Ferraris, M., Reina, C. (1983): Ann. Inst. Henri Poincarè, XXXVIII, N. 4, 371–383

    MathSciNet  Google Scholar 

  30. Geroch, R.P. (1970): J. Math. Phys. 11, 437–449

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Brown, J.D., Lau, S.R., York, J.W.: gr-qc/0010024

    Google Scholar 

  32. Booth, L: gr-qc/0008030

    Google Scholar 

  33. Mangiarotti, L., Sardanashvily, G. (2000) Connections in classical and quantum field theory. World Scientific, Singapore

    Google Scholar 

  34. Ferraris, M., Francaviglia, M., Robutti, O. (1984): In Atti del VI convegno nazionale di Relatività Generale e Fisica della Gravitazione, ed. by M. Modugno, Pitagora, Bologna, pp.137–150

    Google Scholar 

  35. Fatibene, L., Ferraris, ML, Francaviglia, M., Raiteri, M. (1999): Phys. Rev. D 60, 124012, 124013; gr-qc/9902063, gr-qc/9902065

    Article  MathSciNet  ADS  Google Scholar 

  36. Fatibene, L., Ferraris, M., Francaviglia, M., Raiteri, M. (2000): Annals of Phys. 197, 2; gr-qc/9906114

    MathSciNet  Google Scholar 

  37. Mann, R.B., Potvin, G., Raiteri, M. (2000): Class. Quantum Grav. 17, 23

    MathSciNet  Google Scholar 

  38. Landau, L., Lifchitz, L. (1970): Statistical mechanics. 3rd edition, MIR, Moscow

    Google Scholar 

  39. Hawking, S.W., Hunter, C.J., Page, D.N.: hep-th/9809035

    Google Scholar 

  40. Hawking, S.W., Hunter, C.J.: hep-th/9808085 and hep-th/9807010

    Google Scholar 

  41. Allemandi, G., Fatibene, L., Francaviglia, M.: Remarks on the entropy of non stationary black holes. J. Math. Phys.

    Google Scholar 

  42. Gibbons, G.W., Hawking, S.W. (1977): Phys. Rev. D15, 2752

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via C. Alberto 10, 10123, Torino, Italy

    G. Allemandi, L. Fatibene, M. Francaviglia & M. Raiteri

Authors
  1. G. Allemandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Fatibene
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Ferraris
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Francaviglia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Raiteri
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici (DIMET), Università di Genova, Genova, Italy

    R. Cianci

  2. Dipartimento di Fisica, Università di Genova and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Genova, Italy

    R. Collina

  3. Dipartimento di Matematica, Università di Torino, Torino, Italy

    M. Francaviglia

  4. Dipartimento di Fisica Teorica, Università di Torino and Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Torino, Italy

    P. Fré

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Italia

About this paper

Cite this paper

Allemandi, G., Fatibene, L., Ferraris, M., Francaviglia, M., Raiteri, M. (2002). Nöther Conserved Quantities and Entropy in General Relativity. In: Cianci, R., Collina, R., Francaviglia, M., Fré, P. (eds) Recent Developments in General Relativity, Genoa 2000. Springer, Milano. https://doi.org/10.1007/978-88-470-2101-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-88-470-2101-3_6

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-0162-6

  • Online ISBN: 978-88-470-2101-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation