Abstract
We consider the gravitational properties of a global monopole on the basis of the simplest Higgs scalar triplet model in general relativity. We begin with establishing some common features of hedgehog-type solutions with a regular center, independent of the choice of the symmetry-breaking potential. There are six types of qualitative behaviors of the solutions; we show, in particular, that the metric can contain at most one simple horizon. For the standard Mexican hat potential, the previously known properties of the solutions are confirmed and some new results are obtained. Thus, we show analytically that solutions with the monotonically growing Higgs field and finite energy in the static region exist only in the interval 1 < λ < 3, where λ is the squared energy of spontaneous symmetry breaking in Planck units. The cosmological properties of these globally regular solutions apparently favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition at the Planck energy scale. In addition to the monotonic solutions, we present and analyze a sequence of families of new solutions with the oscillating Higgs field. These families are parametrized by n, the number of knots of the Higgs field, and exist for λ < γn=6/[(2n + 1)(n + 2)]; all such solutions possess a horizon and a singularity beyond it.
Similar content being viewed by others
References
Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics (Nauka, Moscow, 1967; Univ. of Chicago Press, Chicago, 1971).
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge Univ. Press, Cambridge, 1994).
T. W. B. Kibble, J. Phys. A 9, 1387 (1976).
A. M. Polyakov, Pis’ma Zh. Éksp. Teor. Fiz. 20, 430 (1974) [JETP Lett. 20, 194 (1974)].
G.’t Hooft, Nucl. Phys. B 79, 276 (1974).
M. Barriola and A. Vilenkin, Phys. Rev. Lett. 63, 341 (1989).
D. Harari and C. Lousto, Phys. Rev. D 42, 2626 (1990).
S. L. Liebling, Phys. Rev. D 61, 024030 (1999).
N. Sakai, H. Shinkai, T. Tachizawa, and K. Maeda, Phys. Rev. D 53, 655 (1996).
A. Vilenkin, Phys. Rev. Lett. 72, 3137 (1994).
A. Linde, Phys. Lett. B 327, 208 (1994).
R. Basu and A. Vilenkin, Phys. Rev. D 50, 7150 (1994).
B. E. Meierovich, Gen. Relativ. Gravit. 33, 405 (2001).
B. E. Meierovich and E. R. Podolyak, Gravit. Cosmology 7, 117 (2001).
K. A. Bronnikov, G. Clément, C. P. Constantinidis, and J. C. Fabris, Phys. Lett. A 243, 121 (1998); gr-qc/9801050; Gravit. Cosmology 4, 128 (1998); gr-qc/9804064.
K. A. Bronnikov, Phys. Rev. D 64, 064013 (2001).
A. S. Kompaneets and A. S. Chernov, Zh. Éksp. Teor. Fiz. 47, 1939 (1964) [Sov. Phys. JETP 20, 1303 (1965)].
R. Kantowski and R. K. Sachs, J. Math. Phys. 7, 443 (1966).
K. A. Bronnikov, Acta Phys. Pol. B 4, 251 (1973).
B. E. Meierovich, Zh. Éksp. Teor. Fiz. 112, 385 (1997) [JETP 85, 209 (1997)]; Gravit. Cosmology 3, 29 (1997); Phys. Rev. D 61, 024004 (2000).
B. E. Meierovich and E. R. Podolyak, Phys. Rev. D 61, 125 007 (2000).
B. E. Meierovich, Usp. Fiz. Nauk 171, 1003 (2001) [Phys. Usp. 44, 981 (2001)].
K. A. Bronnikov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 6, 32 (1979).
M. O. Katanaev, Nucl. Phys. (Proc. Suppl.) 88, 233 (2000); gr-qc/9912039; Proc. Steklov Inst. Math. 228, 158 (2000); gr-qc/9907088.
T. Klosch and T. Strobl, Class. Quantum Grav. 13, 1395 (1996); 14, 1689 (1997).
K. A. Bronnikov and G. N. Shikin, Itogi Nauki Tekh., Ser. Klas. Teor. Polya Gravit. 2, 4 (1991).
E. B. Gliner, Usp. Fiz. Nauk 172, 221 (2002).
E. B. Gliner and I. G. Dymnikova, Pis’ma Astron. Zh. 1(5), 7 (1975) [Sov. Astron. Lett. 1, 93 (1975)]; Usp. Fiz. Nauk 172, 227 (2002).
I. G. Dymnikova, Zh. Éksp. Teor. Fiz. 90, 1900 (1986) [Sov. Phys. JETP 63, 1111 (1986)].
I. Dymnikova and M. Khlopov, Gravit. Cosmol. 4, 50 (1998); Mod. Phys. Lett. A 15, 2305 (2000); Eur. Phys. J. C 20, 139 (2001).
Author information
Authors and Affiliations
Additional information
From Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 122, No. 3, 2002, pp. 459–471.
Original English Text Copyright © 2002 by Bronnikov, Meierovich, Podolyak.
This article was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Bronnikov, K.A., Meierovich, B.E. & Podolyak, E.R. Global monopole in general relativity. J. Exp. Theor. Phys. 95, 392–403 (2002). https://doi.org/10.1134/1.1513811
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1513811