General Relativity and Gravitation

, Volume 21, Issue 11, pp 1093–1098 | Cite as

Do Harrison transformations possess any physical meaning?

  • F. Fayos
  • E. Fornells
  • J. A. Lobo
Research Articles


We propose to give a physical interpretation of the Harrison transformations, so far considered merely as generation techniques of exact solutions of the Einstein-Maxwell equations, as the mechanism which makes a certain class of electrovacuum test fields (Papapetrou fields) gravitate themselves.


Exact Solution Test Field Physical Meaning Differential Geometry Physical Interpretation 
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  1. 1.
    Ernst, F. J. (1968).Phys. Rev.,167, 1175;Phys. Rev.,168, 1415.Google Scholar
  2. 2.
    Neugebauer, G., and Kramer, D. (1969).Ann. Phys.,24, 62.Google Scholar
  3. 3.
    An excellent review is Kramer, D., Stephani, H., McCallum, M., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge). The equivalencei(η)dη =-1/2 [Eqs. (5)-(7)] can be found in Section 30.3.1 of this book.Google Scholar
  4. 4.
    Harrison, B. K. (1968).J. Math. Phys.,9, 1744.Google Scholar
  5. 5.
    Kinnersley, W. (1973).J. Math. Phys.,14, 651.Google Scholar
  6. 6.
    One can find these identities in a general textbook such as Burke, W. L. (1985).Applied Differential Geometry (Cambridge University Press, Cambridge), (i1) and (i2) are introduced when defining the Lie derivative on p. 158. (i3) is proved on pp. 169–170.Google Scholar
  7. 7.
    Given a nonnull vector fieldU, a self-dual bivectorX is completely determined by the projection Z = i(U)X (a) according to the equationX=h−1(U Z). (b), whereh isU's squared modulus.X in Eq. (b) satisfies (a) by direct substitution. Replacing Z, given by (a), into the right-hand side of (b), we get h−1[U. i(U)X]. =h−1i(U)X+ j * [Ui(U)X] = h−1i(U)X-*[U i(U)*x]= h−1^.i(U)X- *[U (X U)] = h−1[U i(U)X+i(U)*(X (U)] = h−1[U i(U)X+ i(U) (X U)] =X, taking into account thatX = j * X, and ** = 1 for 3-forms. In Section 3 we prove that dF=ℒ, F=0 impliesZ = dψ. Google Scholar
  8. 8.
    Papapetrou, A. (1966).Ann. Inst. H. Poincaré,IV, 83.Google Scholar
  9. 9.
    Ernst, F. J., and Wild, W. J. (1976).J. Math. Phys.,17, 182.Google Scholar
  10. 10.
    See Ref. 3 An excellent review is., Section 30.5.2.Google Scholar
  11. 11.
    Rainich, G. Y. (1925).Trans. Am. Math. Soc.,27, 106.Google Scholar
  12. 12.
    Wald, R. M. (1974).Phys. Rev.,D10, 1680.Google Scholar
  13. 13.
    Ernst, F. J. (1976).J. Math. Phys.,17, 54.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • F. Fayos
    • 1
    • 2
  • E. Fornells
    • 1
    • 3
  • J. A. Lobo
    • 1
    • 3
  1. 1.Grup de Relativitat de l'Institut d'Estudis CatalansSocietat Catalana de CiènciesBarcelonaSpain
  2. 2.Departament de Fisica Aplicada de la UPCUniversitat de BarcelonaBarcelonaSpain
  3. 3.Departament de Fisica FonamentalUniversitat de BarcelonaBarcelonaSpain

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