Publication: Integrability formulation and bäcklund-transformations for gravitational-fields with symmetries
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1981
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Amer Physical Soc
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Abstract
The Ernst equation for gravitational fields with a two-parameter isometry group is formulated as a vanishing-curvature condition on an SU(2) or SU(1,1) bundle, both in the elliptic and hyperbolic cases. Bäcklund transformations are introduced as a special case of gauge transformations, and strong Bäcklund transformations are obtained in that context.
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© American Physical Society
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1. D. Maison, Phys. Rev. Lett. 41, 521 (1978);J. Math. Phys. 20, 871 (1979).
2. N, Papanicolaou, J. Math. Phys. 20, 2069 (1979).
3. F. J. Ernst, Phys. Rev. 167, 1175 (1968).
4. Equation (5) has been written as the integrability condition for a nonmanifestly group- covariant linear system in G. Neugebauer, Phys. Lett. 75A, 259 (1980).
5. M. Crampin, Phys. Lett. 66A, 170 (1978).
6. R. Sasaki, Nucl. Phys. B154, 343 (1979).
7. F. J. Chinea, J. Math. Phys. 21, 1588 (1980).
8. Bäcklund transformations for the Ernst equation (5) in the case τ_z ≠ 0 have been investigated in B. K. Harrison, Phys. Rev. Lett. 41, 1197 (1978); 41, 1835(E) (1978).
9. F. J. Chinea, Lett. Math. Phys. (to be published).