Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-08
Nucl.Phys.B843:413-428,2011
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, references added
Scientific paper
10.1016/j.nuclphysb.2010.10.006
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 leads 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.
Chemissany Wissam
Riet Thomas Van
Rosseel Jan
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