Dilatonic monopoles and “hairy” black holes

Y. Brihaye; B. Hartmann; J. Kunz

doi:10.1103/PhysRevD.65.024019

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Dilatonic monopoles and “hairy” black holes

Y. Brihaye

B. Hartmann and J. Kunz

Physique-Mathématique, Université de Mons-Hainaut, Mons, Belgium

Fachbereich Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany

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Phys. Rev. D 65, 024019 – Published 21 December, 2001

DOI: https://doi.org/10.1103/PhysRevD.65.024019

Abstract

We study gravitating monopoles and non-Abelian black holes of SU(2) Einstein-Yang-Mills-Higgs theory coupled to a massless dilaton. The domain of existence of these solutions is bounded and decreases with increasing dilaton coupling strength. The critical solutions of this system are Einstein-Maxwell-dilaton solutions.

References (26)

K. Lee, V. P. Nair, and E. J. Weinberg, Phys. Rev. D 45, 2751 (1992).
P. Breitenlohner, P. Forgacs, and D. Maison, Nucl. Phys. B383, 357 (1992); B442, 126 (1995).
A. Lue and E. J. Weinberg, Phys. Rev. D 60, 084025 (1999); Y. Brihaye, B. Hartmann, and J. Kunz, 62, 044008 (2000).
G. ’t Hooft, Nucl. Phys. B79, 276 (1974); A. M. Polyakov, Pis’ma Zh. Eksp. Teor. Fiz. 20, 430 (1974) [JETP Lett. 20, 194 (1974)].
J. A. Frieman and C. T. Hill, SLAC Report No. SLAC-PUB-4283, 1987.
For vanishing and small Higgs boson mass $α_{cr} <~ α_{\max}$ [2], while for large Higgs boson mass the Lue-Weinberg phenomenon occurs [3].
P. C. Aichelburg and P. Bizon, Phys. Rev. D 48, 607 (1993).
A. Ashtekar, A. Corichi, and D. Sudarsky, Class. Quantum Grav. 18, 919 (2001).
D. Nunez, H. Quevedo, and D. Sudarsky, Phys. Rev. Lett. 76, 571 (1996).
P. Forgacs and J. Gyueruesi, Phys. Lett. B 366, 205 (1996).
J. A. Harvey and J. Liu, Phys. Lett. B 268, 40 (1991); J. P. Gauntlett, J. A. Harvey, and J. Liu, Nucl. Phys. B409, 363 (1993).
G. W. Gibbons and K. Maeda, Nucl. Phys. B298, 741 (1988); D. Garfinkle, G. T. Horowitz, and A. Strominger, Phys. Rev. D 43, 3140 (1991).
B. Kleihaus, J. Kunz, and A. Sood, Phys. Rev. D 54, 5070 (1996).
B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975).
Y. Brihaye, B. Hartmann, and J. Kunz, Phys. Lett. B 441, 77 (1998); Y. Brihaye, B. Hartmann, J. Kunz, and Nadege Tell, Phys. Rev. D 60, 104016 (1999).
The equations of motion are invariant under a shift $ψ \to ψ + ψ_{0},$ together with a rescaling $x \to {xe}^{γ ψ_{0}} .$ Therefore solutions regular at infinity can always be chosen to satisfy $ψ (\infty) = 0.$
For larger values of β, the non-Abelian monopole solutions do not bifurcate with a branch of Abelian solutions at $α_{cr} .$ Instead the critical solution is essentially non-Abelian [3].
Similarly, Einstein-Yang-Mills-dilaton solutions tend to an Einstein-Maxwell-dilaton solution (in the limit of a large node number) [13], while Einstein-Yang-Mills solutions tend to an Einstein-Maxwell (RN) solution.
For instance, for $α = 1$ we find $γ_{\max} (α = 1) = 0.9872,$ which is very close to $α_{\max} (γ = 1) = 0.9882.$
G. Lavrelashvili and D. Maison, Nucl. Phys. B410, 407 (1993).
For $γ = 0.5,$ the determination of $α_{\max}$ becomes numerically unreliable for $β > 6;$ for $γ = 1,$ the analysis becomes problematic already for $β = 3.$
With increasing β, the dilaton function $ψ (x)$ develops a minimum close to the origin, with strongly increasing curvature.
We expect that for $γ \to 1.4088,$ the maximal value of γ for which regular solutions of the YMHD theory exist, the domain of existence shrinks to zero size.
B. Hartmann, B. Kleihaus, and J. Kunz, Phys. Rev. Lett. 86, 1422 (2001); Phys. Rev. D (to be published), hep-th/0108129.
S. A. Ridgway and E. J. Weinberg, Phys. Rev. D 52, 3440 (1995).
U. Ascher, J. Christiansen, and R. D. Russell, Math. Comput. 33, 659 (1979); ACM Trans. Math. Softw. 7, 209 (1981).

[c1] K. Lee, V. P. Nair, and E. J. Weinberg, Phys. Rev. D 45, 2751 (1992).

[c2] P. Breitenlohner, P. Forgacs, and D. Maison, Nucl. Phys. B383, 357 (1992); B442, 126 (1995).

[c3] A. Lue and E. J. Weinberg, Phys. Rev. D 60, 084025 (1999); Y. Brihaye, B. Hartmann, and J. Kunz, 62, 044008 (2000).

[c4] G. ’t Hooft, Nucl. Phys. B79, 276 (1974); A. M. Polyakov, Pis’ma Zh. Eksp. Teor. Fiz. 20, 430 (1974) [JETP Lett. 20, 194 (1974)].

[c5] J. A. Frieman and C. T. Hill, SLAC Report No. SLAC-PUB-4283, 1987.

[c6] For vanishing and small Higgs boson mass $α_{cr} <~ α_{\max}$ [2], while for large Higgs boson mass the Lue-Weinberg phenomenon occurs [3].

[c7] P. C. Aichelburg and P. Bizon, Phys. Rev. D 48, 607 (1993).

[c8] A. Ashtekar, A. Corichi, and D. Sudarsky, Class. Quantum Grav. 18, 919 (2001).

[c9] D. Nunez, H. Quevedo, and D. Sudarsky, Phys. Rev. Lett. 76, 571 (1996).

[c10] P. Forgacs and J. Gyueruesi, Phys. Lett. B 366, 205 (1996).

[c11] J. A. Harvey and J. Liu, Phys. Lett. B 268, 40 (1991); J. P. Gauntlett, J. A. Harvey, and J. Liu, Nucl. Phys. B409, 363 (1993).

[c12] G. W. Gibbons and K. Maeda, Nucl. Phys. B298, 741 (1988); D. Garfinkle, G. T. Horowitz, and A. Strominger, Phys. Rev. D 43, 3140 (1991).

[c13] B. Kleihaus, J. Kunz, and A. Sood, Phys. Rev. D 54, 5070 (1996).

[c14] B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975).

[c15] Y. Brihaye, B. Hartmann, and J. Kunz, Phys. Lett. B 441, 77 (1998); Y. Brihaye, B. Hartmann, J. Kunz, and Nadege Tell, Phys. Rev. D 60, 104016 (1999).

[c16] The equations of motion are invariant under a shift $ψ \to ψ + ψ_{0},$ together with a rescaling $x \to {xe}^{γ ψ_{0}} .$ Therefore solutions regular at infinity can always be chosen to satisfy $ψ (\infty) = 0.$

[c17] For larger values of β, the non-Abelian monopole solutions do not bifurcate with a branch of Abelian solutions at $α_{cr} .$ Instead the critical solution is essentially non-Abelian [3].

[c18] Similarly, Einstein-Yang-Mills-dilaton solutions tend to an Einstein-Maxwell-dilaton solution (in the limit of a large node number) [13], while Einstein-Yang-Mills solutions tend to an Einstein-Maxwell (RN) solution.

[c19] For instance, for $α = 1$ we find $γ_{\max} (α = 1) = 0.9872,$ which is very close to $α_{\max} (γ = 1) = 0.9882.$

[c20] G. Lavrelashvili and D. Maison, Nucl. Phys. B410, 407 (1993).

[c21] For $γ = 0.5,$ the determination of $α_{\max}$ becomes numerically unreliable for $β > 6;$ for $γ = 1,$ the analysis becomes problematic already for $β = 3.$

[c22] With increasing β, the dilaton function $ψ (x)$ develops a minimum close to the origin, with strongly increasing curvature.

[c23] We expect that for $γ \to 1.4088,$ the maximal value of γ for which regular solutions of the YMHD theory exist, the domain of existence shrinks to zero size.

[c24] B. Hartmann, B. Kleihaus, and J. Kunz, Phys. Rev. Lett. 86, 1422 (2001); Phys. Rev. D (to be published), hep-th/0108129.

[c25] S. A. Ridgway and E. J. Weinberg, Phys. Rev. D 52, 3440 (1995).

[c26] U. Ascher, J. Christiansen, and R. D. Russell, Math. Comput. 33, 659 (1979); ACM Trans. Math. Softw. 7, 209 (1981).

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Dilatonic monopoles and “hairy” black holes

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