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Landau-Lifshitz solutions of , supergravity
Phys. Rev. D 112, 024009 – Published 7 July, 2025
DOI: https://doi.org/10.1103/8qrd-1hz6
Abstract
We study families of solutions depending only on one coordinate for the theories of , five-dimensional supergravity coupled to vector multiplets. Four families of solutions, valid for all space-time signatures, are obtained. The explicit metrics of the solutions depend on the Jordan normal forms of constrained matrices. Examples with three charges are given for the so-called STU model.
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References (26)
- E. Kasner, Geometrical theorems on Einstein’s cosmological equations, Am. J. Math. 43, 217 (1921).
- A. Harvey, Complex transformation of the Kasner metric, Gen. Relativ. Gravit., 21, 1021 (1989).
- G. F. R. Ellis and M. A. H. MacCallum, A class of homogeneous cosmological models, Commun. Math. Phys. 12, 108 (1969).
- L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, Amsterdam, Boston, Oxford, 1980).
- E. M. Lifshitz and I. M. Khalatnikov, Investigations in relativistic cosmology, Adv. Phys. 12, 185 (1963).
- V. A. Belinski and I. M. Khalatnikov, Effect of scalar and vector fields on the nature of the cosmological singularity, Sov. Phys. JETP 36, 591 (1973).
- F. Dowker, J. P. Gauntlett, D. A. Kastor, and J. H. Traschen, Pair creation of dilaton black holes, Phys. Rev. D 49, 2909 (1994).
- D. Kastor and J. Traschen, Melvin magnetic fluxtube/cosmology correspondence, Classical Quantum Gravity 32, 235027 (2015).
- B. K. Harrison, New solutions of the Einstein-Maxwell equations from old, J. Math. Phys. (N.Y.) 9, 1744 (1968).
- F. J. Ernst, Black holes in a magnetic universe, J. Math. Phys. (N.Y.) 17, 54 (1976).
- W. A. Sabra, Kasner branes with arbitrary signature, Phys. Lett. B 809, 135694 (2020).
- W. A. Sabra, Kasner metrics and very special geometry, Phys. Lett. B 833, 137380 (2022).
- W. A. Sabra, Melvin space-times in supergravity, Phys. Lett. B 847, 138307 (2023).
- W. A. Sabra, Metrics depending on one variable in Einstein-Maxwell theory, Phys. Rev. D 110, 064080 (2024).
- M. Fakherdin and W. A. Sabra, One-variable metrics in string theory, Phys. Rev. D 111, 106001 (2025).
- M. A. Melvin, Pure magnetic and electric geons, Phys. Lett. 8, 65 (1964); G. Rosen, Symmetries of the Einstein-Maxwell equations, J. Math. Phys. (N.Y.) 3, 313 (1962); Spatially homogeneous solutions to the Einstein-Maxwell equations, Phys. Rev. 136, B297 (1964).
- V. Belinski and M. Henneaux, The Cosmological Singularity (Cambridge University Press, Cambridge, England, 2017).
- M. Gunaydin, G. Sierra, and P. K. Townsend, The geometry of Maxwell-Einstein supergravity and Jordan algebras, Nucl. Phys. B242, 244 (1984).
- E. Lauria and A. Van Proeyen, N=2 Supergravity in D=4, 5, 6 Dimensions, Lecture Notes in Physics (Springer Cham, 2020).
- A. Ceresole, R. D’Auria, and S. Ferrara, 11-dimensional supergravity compactified on Calabi-Yau threefolds, Phys. Lett. B 357, 76 (1995).
- E. Cremmer, B. Julia, and J. Scherk, Supergravity theory in eleven-dimensions, Phys. Lett. 76B, 409 (1978).
- W. A. Sabra and O. Vaughan, Euclidean supergravity in five dimensions, Phys. Lett. B 760, 14 (2016).
- W. A. Sabra, Special geometry and space-time signature, Phys. Lett. B 773, 191 (2017).
- L. Gall and T. Mohaupt, Five-dimensional vector multiplets in arbitrary signature, J. High Energy Phys. 09 (2018) 053.
- C. M. Hull, Duality and the signature of space-time, J. High Energy Phys. 11 (1998) 017.
- R. Emparan and H. S. Reall, Black rings, Classical Quantum Gravity 23, R169 (2006).