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The Yamabe invariant for axially symmetric initial data of two Kerr black holes

2008; IOP Publishing; Volume: 25; Issue: 22 Linguagem: Inglês

10.1088/0264-9381/25/22/225002

1361-6382

Gastón A Avila, Sergio Dain,

Cosmology and Gravitation Theories

An explicit three-dimensional Riemannian metric is constructed which can be interpreted as the (conformal) sum of two Kerr black holes with aligned angular momenta. When the separation distance between them is large we prove that this metric has a positive Ricci scalar and hence a positive Yamabe invariant. This metric can be used to construct axially symmetric initial data for two Kerr black holes with large total angular momentum.