Charges from Attractors
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We describe how to recover the quantum numbers of extremal black holes from their near horizon geometries. This is achieved by constructing the gravitational Noether-Wald charges which can be used for non-extremal black holes as well. These charges are shown to be equivalent to the U(1) charges of appropriately dimensionally reduced solutions. Explicit derivations are provided for 10 dimensional type IIB supergravity and 5 dimensional minimal gauged supergravity, with illustrative examples for various black hole solutions. We also discuss how to derive the thermodynamic quantities and their relations explicitly in the extremal limit, from the point of view of the near-horizon geometry. We relate our results to the entropy function formalism.
25 pages; references and comments added, typos fixed, minor changes to notation, minor clarifications in the discussions; final version published in CQG
25 pages; references and comments added, typos fixed, minor changes to notation, minor clarifications in the discussions; final version published in CQG