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Black rings with fourth dipole cause less hair loss

An example of entropy enigma with a controlled CFT dual was recently studied in arXiv:1108.0411. The enigmatic bulk configurations, considered within the STU model, can be mapped under spectral flow into black rings with three monopole and dipole charges. Even though the bulk and CFT configurations existed in the same region of parameter space, the Bekenstein-Hawking entropy of the bulk configurations was found to be lower than the microscopic entropy from the CFT. While it is possible that the difference in entropy is due to the bulk and boundary configurations being at different points in the moduli space, it is also possible that the bulk configurations embeddable within the STU model are not the most entropic. New families of BPS black ring solutions with four electric and four dipole magnetic charges have recently been explicitly constructed in arXiv:1201.2585. These black rings are not embeddable within the STU model. In this paper we investigate if these black rings can be entropically dominant over the STU model black rings. We find that the new black rings are always entropically subdominant to the STU-model black rings. However, for small fourth dipole charge these black rings continue to be dominant over the BMPV in a small region of parameters and are thus enigmatic.