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|Paper IPM / P / 14651||
Black holes as solutions to gravity theories, are generically identified by a set of parameters. Some of these parameters are associated with black hole physical conserved charges, like ADM charges. There can also be some "redundant parameters." We propose necessary conditions for a parameter to be physical. The conditions are essentially integrability and non-triviality of the charges variations arising from "parametric variations," variation of the solution with respect to the chosen parameters. In addition, we prove that variation of the redundant parameters which are rejected by our criterion do not appear in the first law of thermodynamics. As an interesting application, we show that dilaton moduli are redundant parameters for black hole solutions to Einstein-Maxwell-(Axion)-Dilaton theories, because variations in dilaton moduli would render entropy, mass, electric charge and angular momentum non-integrable. Our results are in contrast with modification of the first law due to scalar charges suggested in Gibbons-Kallosh-Kol paper [arXiv:hep-th/9607108] and its follow-ups. We also briefly discuss implications of our results for the attractor behavior of extremal black holes.
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