Regular magnetic black holes and monopoles from nonlinear electrodynamics

K. A. Bronnikov

doi:10.1103/PhysRevD.63.044005

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Regular magnetic black holes and monopoles from nonlinear electrodynamics

K. A. Bronnikov^*

Centre for Gravitation and Fundam. Metrology, VNIIMS, 3-1 M. Ulyanovoy St., Moscow 117313, Russia
Institute of Gravitation and Cosmology, PFUR, 6 Miklukho-Maklaya St., Moscow 117198, Russia

^*Email address: kb@rgs.mccme.ru

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Phys. Rev. D 63, 044005 – Published 17 January, 2001

DOI: https://doi.org/10.1103/PhysRevD.63.044005

Abstract

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L (F),$ ${F = F}_{μ ν} F^{μ ν}$ having a correct weak field limit, leads to nontrivial spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and $L (F)$ tends to a finite limit as $\vec{F} \infty .$ The properties and examples of such solutions, which include magnetic black holes and solitonlike objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called the $FP$ duality) is used as a tool for this comparison.

References (19)

K. A. Bronnikov and G. N. Shikin, in Results of Science and Technology: Classical Field Theory and Gravitation Theory (VINITI, Moscow, 1991), Vol. 2, p. 4.
J. A. Smoller and A. G. Wassermann, Commun. Math. Phys. 151, 303 (1993); ibid.P. Breitenlohner, P. Forgács, and D. Maison, 163, 141 (1994).
I. Dymnikova, Gen. Relativ. Gravit. 24, 235 (1992).
I. Dymnikova, Phys. Lett. B 472, 33 (2000); gr-qc/0010016.
N. Seiberg and E. Witten, J. High Energy Phys. 09, 032 (1999); A. A. Tseytlin, hep-th/9908105.
K. A. Bronnikov and G. N. Shikin, in Classical and Quantum Theory of Gravity, Trudy IF AN BSSR, Minsk, 1976, p. 88.
K. A. Bronnikov, V. N. Melnikov, G. N. Shikin, and K. P. Staniukovich, Ann. Phys. (N.Y.) 118, 84 (1979).
E. Ayón-Beato and A. García, Phys. Rev. Lett. 80, 5056 (1998).
E. Ayón-Beato and A. García, Phys. Lett. B 464, 25 (1999).
E. Ayón-Beato and A. García, Gen. Relativ. Gravit. 31, 629 (1999).
H. Salazar, A. García, and J. Plebański, J. Math. Phys. 28, 2171 (1987).
T. Banks, A. Dabholkar, M. R. Douglas, and M. O’Loughlin, Phys. Rev. D 45, 3607 (1992); ibid.T. Banks and M. O’Loughlin, 47, 540 (1993).
D. Hochberg and M. Visser, Phys. Rev. D 56, 4745 (1997).
N. Rosen and H. B. Rosenstock, Phys. Rev. 85, 257 (1952).
Yu. P. Rybakov, Particle Structure in Nonlinear Field Theory (Peoples’ Friendship University Press, Moscow, 1985).
G. W. Gibbons and D. A. Rasheed, Nucl. Phys. B454, 185 (1995).
M. Novello, V. A. de Lorenci, J. M. Salim, and R. Klippert, Phys. Rev. D 61, 045001 (2000).
M. Novello, S. E. Perez Bergliaffa, and J. M. Salim, Class. Quantum Grav. 17, 3821 (2000).
P. A. M. Dirac, Proc. R. Soc. London A209, 291 (1951).

[c1] K. A. Bronnikov and G. N. Shikin, in Results of Science and Technology: Classical Field Theory and Gravitation Theory (VINITI, Moscow, 1991), Vol. 2, p. 4.

[c2] J. A. Smoller and A. G. Wassermann, Commun. Math. Phys. 151, 303 (1993); ibid.P. Breitenlohner, P. Forgács, and D. Maison, 163, 141 (1994).

[c3] I. Dymnikova, Gen. Relativ. Gravit. 24, 235 (1992).

[c4] I. Dymnikova, Phys. Lett. B 472, 33 (2000); gr-qc/0010016.

[c5] N. Seiberg and E. Witten, J. High Energy Phys. 09, 032 (1999); A. A. Tseytlin, hep-th/9908105.

[c6] K. A. Bronnikov and G. N. Shikin, in Classical and Quantum Theory of Gravity, Trudy IF AN BSSR, Minsk, 1976, p. 88.

[c7] K. A. Bronnikov, V. N. Melnikov, G. N. Shikin, and K. P. Staniukovich, Ann. Phys. (N.Y.) 118, 84 (1979).

[c8] E. Ayón-Beato and A. García, Phys. Rev. Lett. 80, 5056 (1998).

[c9] E. Ayón-Beato and A. García, Phys. Lett. B 464, 25 (1999).

[c10] E. Ayón-Beato and A. García, Gen. Relativ. Gravit. 31, 629 (1999).

[c11] H. Salazar, A. García, and J. Plebański, J. Math. Phys. 28, 2171 (1987).

[c12] T. Banks, A. Dabholkar, M. R. Douglas, and M. O’Loughlin, Phys. Rev. D 45, 3607 (1992); ibid.T. Banks and M. O’Loughlin, 47, 540 (1993).

[c13] D. Hochberg and M. Visser, Phys. Rev. D 56, 4745 (1997).

[c14] N. Rosen and H. B. Rosenstock, Phys. Rev. 85, 257 (1952).

[c15] Yu. P. Rybakov, Particle Structure in Nonlinear Field Theory (Peoples’ Friendship University Press, Moscow, 1985).

[c16] G. W. Gibbons and D. A. Rasheed, Nucl. Phys. B454, 185 (1995).

[c17] M. Novello, V. A. de Lorenci, J. M. Salim, and R. Klippert, Phys. Rev. D 61, 045001 (2000).

[c18] M. Novello, S. E. Perez Bergliaffa, and J. M. Salim, Class. Quantum Grav. 17, 3821 (2000).

[c19] P. A. M. Dirac, Proc. R. Soc. London A209, 291 (1951).

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Regular magnetic black holes and monopoles from nonlinear electrodynamics

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