Geodesic
Symmetry orbits of supergravity black holes
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 158-170

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Black-hole solutions of supergravity theories form families that realize the deep nonlinear “duality” symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e., BPS) solutions at the limits of such orbits. An important technique for analyzing such solution families uses timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. We characterize families of extremal or BPS solutions by nilpotent orbits under the duality symmetries, based on a trigraded or pentagraded decomposition of the corresponding duality-group algebra.
Keywords: black hole, duality symmetry, sigma model. 
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     author = {K. S. Stelle},
     title = {Symmetry orbits of supergravity black holes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {158--170},
     publisher = {mathdoc},
     volume = {182},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a9/}
}
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K. S. Stelle. Symmetry orbits of supergravity black holes. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 158-170. http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a9/