Regular solution of 't Hooft's magnetic monopole model in curved space

P. van Nieuwenhuizen; David Wilkinson; M. J. Perry

doi:10.1103/PhysRevD.13.778

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Regular solution of 't Hooft's magnetic monopole model in curved space

P. van Nieuwenhuizen and David Wilkinson

M. J. Perry

Institute for Theoretical Physics at State University of New York, Stony Brook, New York 11794

DAMTP, Cambridge, England

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Phys. Rev. D 13, 778 – Published 15 February, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.778

Abstract

A regular solution of 't Hooft's magnetic monopole model in curved space is presented. As in flat space, an analytical solution seems impossible, but by using the Einstein equations to eliminate the gravitational degrees of freedom, a positive-definite energy functional is constructed, which at its minimum gives both the required solution and the energy of the system. To first order in the gravitational constant $G$ , the energy can be expressed in terms of the flat-space solutions only, whereas for general $G$ a positive lower bound is derived.

References (16)

G. 't Hooft, Nucl. Phys. B79, 276 (1974)
M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)
F. A. Bais and R. J. Russell, Phys. Rev. D 11, 2692 (1975)
Y. M. Cho and P. G. O. Freund, Phys. Rev. D 12, 1588 (1975)
P. Cordero and C. Teitelboim (unpublished)
T. T. Wu and C. N. Yang, in Properties of Matter under Unusual Conditions, edited by H. Mark and S. Fernbach (Interscience, New York, 1969)
P. A. M. Dirac, Proc. R. Soc. London A133, 60 (1931)
L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Addison-Wesley, Reading, Mass., 1962)
Omitted endnote
D. R. Brill and S. Deser, Ann. Phys. (N.Y.) 50, 548 (1968)
Omitted endnote
B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975)
[14] [15]
S. Deser, M. T. Grisaru, P. van Nieuwenhuizen, and C. C. Wu (unpublished)
J. Schwinger (unpublished)
J. Arafune, P. G. O. Freund, and C. J. Goebel, J. Math. Phys. 16, 433 (1975)

[c1] G. 't Hooft, Nucl. Phys. B79, 276 (1974)

[c2] M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)

[c3] F. A. Bais and R. J. Russell, Phys. Rev. D 11, 2692 (1975)

[c4] Y. M. Cho and P. G. O. Freund, Phys. Rev. D 12, 1588 (1975)

[c5] P. Cordero and C. Teitelboim (unpublished)

[c6] T. T. Wu and C. N. Yang, in Properties of Matter under Unusual Conditions, edited by H. Mark and S. Fernbach (Interscience, New York, 1969)

[c7] P. A. M. Dirac, Proc. R. Soc. London A133, 60 (1931)

[c8] L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Addison-Wesley, Reading, Mass., 1962)

[c9] Omitted endnote

[c10] D. R. Brill and S. Deser, Ann. Phys. (N.Y.) 50, 548 (1968)

[c11] Omitted endnote

[c12] B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975)

[c13] [14] [15]

[c14] S. Deser, M. T. Grisaru, P. van Nieuwenhuizen, and C. C. Wu (unpublished)

[c15] J. Schwinger (unpublished)

[c16] J. Arafune, P. G. O. Freund, and C. J. Goebel, J. Math. Phys. 16, 433 (1975)

Physical Review D

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Regular solution of 't Hooft's magnetic monopole model in curved space

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