Black holes as generalised Toda molecules |
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Authors: | Wissam Chemissany Jan Rosseel Thomas Van Riet |
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Institution: | 1. University of Lethbridge, Physics Dept., Lethbridge T1K 3M4, Alberta, Canada;2. Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands;3. Institutionen för Fysik och Astronomi, Box 803, SE-751 08 Uppsala, Sweden |
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Abstract: | In this note we compare the geodesic formalism for spherically symmetric black hole solutions with the black hole effective potential approach. The geodesic formalism is beneficial for symmetric supergravity theories since the symmetries of the larger target space lead to a complete set of commuting constants of motion that establish the integrability of the geodesic equations of motion, as shown in arXiv:1007.3209. We point out that the integrability lifts straightforwardly to the integrability of the equations of motion with a black hole potential. This construction turns out to be a generalisation of the connection between Toda molecule equations and geodesic motion on symmetric spaces known in the mathematics literature. We describe in some detail how this generalisation of the Toda molecule equations arises. |
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