Abstract
We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS 2 × S 2 and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen’s entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza–Klein black hole.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Astefanesei, D., Goldstein, K. & Mahapatra, S. Moduli and (un)attractor black hole thermodynamics. Gen Relativ Gravit 40, 2069–2105 (2008). https://doi.org/10.1007/s10714-008-0616-6
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DOI: https://doi.org/10.1007/s10714-008-0616-6