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Twistors and Black Holes

By A. Neitzke, B. Pioline and S. Vandoren


Motivated by black hole physics in N = 2,D = 4 supergravity, we study\ud the geometry of quaternionic-K¨ahler manifolds Mobtained by the c-map construction\ud from projective special Kähler manifolds Ms. Improving on earlier treatments, we\ud compute the Käahler potentials on the twistor space Z and Swann space S in the\ud complex coordinates adapted to the Heisenberg symmetries. The results bear a simple\ud relation to the Hesse potential E of the special Käahler manifold Ms, and hence to\ud the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the\ud “covariant c-map” and the “twistor map”, which relate real coordinates on M× CP1\ud (resp. M×R4/Z2) to complex coordinates on Z (resp. S). As applications, we solve for\ud the general BPS geodesic motion on M, and provide explicit integral formulae for the\ud quaternionic Penrose transform relating elements of H1(Z,O(−k)) to massless fields\ud on M annihilated by first or second order differential operators. Finally, we compute\ud the exact radial wave function (in the supergravity approximation) for BPS black holes\ud with fixed electric and magnetic charges

Topics: Natuur- en Sterrenkunde
Year: 2007
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