Abstract
Four dimensional \( \mathcal{N} = {2} \) supergravity has regular, stationary, asymptotically flat BPS solutions with intrinsic angular momentum, describing bound states of separate extremal black holes with mutually nonlocal charges. Though the existence and some properties of these solutions were established some time ago, fully explicit analytic solutions were lacking thus far. In this note, we fill this gap. We show in general that explicit solutions can be constructed whenever an explicit formula is known in the theory at hand for the Bekenstein-Hawking entropy of a single black hole as a function of its charges, and illustrate this with some simple examples. We also give an example of moduli-dependent black hole entropy.
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References
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [INSPIRE].
G.W. Moore, Arithmetic and attractors, hep-th/9807087 [INSPIRE].
M.R. Douglas, Topics in D geometry, Class. Quant. Grav. 17 (2000) 1057 [hep-th/9910170] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
M.R. Douglas, B. Fiol and C. Romelsberger, Stability and BPS branes, JHEP 09 (2005) 006 [hep-th/0002037] [INSPIRE].
M.R. Douglas, B. Fiol and C. Romelsberger, The spectrum of BPS branes on a noncompact Calabi-Yau, JHEP 09 (2005) 057 [hep-th/0003263] [INSPIRE].
M.R. Douglas, D-branes, categories and N = 1 supersymmetry, J. Math. Phys. 42 (2001) 2818 [hep-th/0011017] [INSPIRE].
F. Denef, B.R. Greene and M. Raugas, Split attractor flows and the spectrum of BPS D-branes on the quintic, JHEP 05 (2001) 012 [hep-th/0101135] [INSPIRE].
K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Käppeli and T. Mohaupt, Stationary BPS solutions in N =2 supergravity with R 2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Käppeli and T. Mohaupt, Examples of stationary BPS solutions in N = 2 supergravity theories with R 2 interactions, Fortsch. Phys. 49 (2001) 557 [hep-th/0012232] [INSPIRE].
F. Denef, On the correspondence between D-branes and stationary supergravity solutions of type-II Calabi-Yau compactifications, hep-th/0010222 [INSPIRE].
B. de Wit and A. Van Proeyen, Potentials and symmetries of general gauged N = 2 supergravity: Yang-Mills models, Nucl. Phys. B 245 (1984) 89 [INSPIRE].
B. Craps, F. Roose, W. Troost and A. Van Proeyen, What is special Kähler geometry?, Nucl. Phys. B 503 (1997) 565 [hep-th/9703082] [INSPIRE].
M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540 [hep-th/9612076] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
C. Vafa, Black holes and Calabi-Yau threefolds, Adv. Theor. Math. Phys. 2 (1998) 207 [hep-th/9711067] [INSPIRE].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].
C. Misner, K. Thorne and J.A. Wheeler, Gravitation, chapter 21, Freeman and co., U.S.A. (1973).
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ArXiv ePrint: hep-th/0304094
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Bates, B., Denef, F. Exact solutions for supersymmetric stationary black hole composites. J. High Energ. Phys. 2011, 127 (2011). https://doi.org/10.1007/JHEP11(2011)127
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DOI: https://doi.org/10.1007/JHEP11(2011)127