Ehlers-Harrison transformations and black holes in dilaton-axion gravity with multiple vector fields

D. V. Gal’tsov; P. S. Letelier

doi:10.1103/PhysRevD.55.3580

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Ehlers-Harrison transformations and black holes in dilaton-axion gravity with multiple vector fields

D. V. Gal’tsov and P. S. Letelier

Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas, 13081-970 Campinas, SP, Brazil

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Phys. Rev. D 55, 3580 – Published 15 March, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.3580

Abstract

Dilaton-axion gravity with $p$ U(1) vector fields is studied on space-times admitting a timelike Killing vector field. A three-dimensional $σ$ model is derived in terms of Kähler geometry, and a holomorphic representation of the SO $(2, 2 + p)$ global symmetry is constructed. A general static black hole solution depending on $2 p + 5$ parameters is obtained via SO $(2, 2 + p)$ covariantization of the Schwarzschild solution. The metric in the curvature coordinates looks like the variable mass Reissner-Nordström one and generically possesses two horizons. The inner horizon is pushed to the singularity if electric and magnetic SO $(p)$ charge vectors are parallel. For nonparallel charges the inner horizon has a finite area except for an extremal limit when this property is preserved only for orthogonal charges. Extremal dyon configurations with orthogonal charges have finite horizon radii continuously varying from zero to the Arnowitt-Deser-Misner mass. The new general solution is endowed with a Newman-Unti-Tamburino parameter, asymptotic values of dilaton and axion, and a gauge parameter which can be used to ascribe any given value to one of the scalar charges.

References (25)

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[c1] G. T. Horowitz, “The Origin of Black Hole Entropy in String Theory, ” Report No. UCSBTH-96-07, Gr-qc/9604951 (unpublished).

[c2] G. W. Gibbons, Nucl. Phys.B207, 337 (1982); G. W. Gibbons and K. Maeda, B298, 741 (1988).

[c3] D. Garfinkle, G. T. Horowitz, and A. Strominger, Phys. Rev. D43, 3140 (1991); 45, 3888(E) (1992).

[c4] G. Clément and D. Gal’tsov, Phys. Rev. D54, 6136 (1996).

[c5] R. Kallosh, A. Linde, T. Ortin, A. Peet, and A. van Proyen, Phys. Rev. D46, 5278 (1992).

[c6] E. Bergshoeff, R. Kallosh, and T. Ortin, Nucl. Phys.B478, 156 (1996).

[c7] R. Kallosh, D. Kastor, T. Ortin, and T. Torma, Phys. Rev. D50, 6374 (1994).

[c8] M. Cvetič and D. Youm, “All the Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus,” Report No. IASSNS-HEP-95-107, Hep-th/9512127 (unpublished); M. Cvetič and A. Tseytlin, Phys. Rev. D53, 5619 (1996); Nucl. Phys.B478, 181 (1996); M. Cvetič and C. M. Hull, B480, 296 (1996).

[c9] K. P. Tod, Phys. Lett.121B, 241 (1983); Class. Quantum Grav.12, 1801 (1995).

[c10] D. Kramer, H. Stephani, M. MacCallum, and E. Herlt, Exact Solutions of the Einstein Field Equations (Cambridge University Press, Cambridge, England, 1980).

[c11] D. V. Gal’tsov and O. V. Kechkin, Phys. Rev. D50, 7394 (1994); D. V. Gal’tsov, Phys. Rev. Lett.74, 2863 (1995); in Heat Kernel Techniques and Quantum Gravity, Proceedings of the Winnipeg Workshop, 1994, edited by S. A. Fulling (Texas A&M University, College Station, 1995), p. 423, Report No. Hep-th/9606042 (unpublished).

[c12] D. V. Gal’tsov and O. V. Kechkin, Phys. Lett. B361, 52 (1995); Phys. Rev. D54, 1656 (1996).

[c13] F. J. Ernst, Phys. Rev.167, 1175 (1968); 168, 1415 (1968); W. Kinnersley, J. Math. Phys. (N.Y.)14, 651 (1973); 18, 1529 (1977).

[c14] P. O. Mazur, Acta Phys. Pol. B14, 219 (1983); A. Eris, M. Gürses, and A. Karasu, J. Math. Phys. (N.Y.)25, 1489 (1984).

[c15] I. Bakas, Nucl. Phys.B428, 374 (1994); Phys. Lett. B343, 103 (1995); Phys. Rev. D54, 6424 (1996).

[c16] D. V. Gal’tsov, Geroch-Kinnersley-Chitre group for Dilaton-Axion Gravity, in Proceedings of the International Workshop, Leipzig, Germany, 18–22 September, 1995, edited by M. Bordag (B. G. Teubner Verlagsgessellschaft, Stuttgart–Leipzig, 1996), pp. 228–237.

[c17] D. V. Gal’tsov, “Square of General Relativity,” Report No. DTP-MSU 96/14, Hep-th/9608021 (unpublished).

[c18] S. Shapere, S. Trivedi, and F. Wilczek, Mod. Phys. Lett. A6, 2677 (1991); A. Sen, Nucl. Phys.B404, 109 (1993); Phys. Lett. B303, 22 (1993); Int. J. Mod. Phys. A8, 5079 (1993); Mod. Phys. Lett. A8, 2023 (1993); J. H. Schwarz and A. Sen, Nucl. Phys.B411, 35 (1994); Phys. Lett. B312, 105 (1993).

[c19] W. Israel and G. A. Wilson, J. Math. Phys. (N.Y.)13, 865 (1972).

[c20] G. Neugebauer and D. Kramer, Ann. Phys. (Leipzig)24, 62 (1969).

[c21] D. Gal’tsov, A. García, and O. Kechkin, J. Math. Phys. (N.Y.)36, 5023 (1995).

[c22] J. Ehlers, in Les Theories Relativistes de la Gravitation (CNRS, Paris, 1959), p. 275.

[c23] D. V. Gal’tsov and P. S. Letelier, Class. Quantum Grav. (to be published).

[c24] P. Breitenlohner, D. Maison, and G. Gibbons, Commun. Math. Phys.120, 253 (1988).

[c25] R. Kallosh, M. Shmakova, and W. K. Wong, Phys. Rev. D54, 6284 (1996); G. Gibbons, R. Kallosh, and B. Kol, Phys. Rev. Lett.77, 4992 (1996).

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Ehlers-Harrison transformations and black holes in dilaton-axion gravity with multiple vector fields

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