1 | See, e.g., [89], p. 239 or [151![]() |
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2 | This theorem was first proven by Schoen and Yau [288, 289] and somewhat later, using spinor techniques, by Witten [325] (compare [265]). See [12] for a version relevant to the uniqueness problem, which allows degenerate components of the event horizon. | |
3 | Non-existence of certain static ![]() ![]() ![]() |
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4 | Here we are interested in stationary multi–black-hole configurations; nonexistence of some suitably regular stationary
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5 | Studies of regularity and causal structure of black rings and Saturns can be found in [82, 67, 68, 305, 71]. | |
6 | It should be noted that, although formulated for 4-dimensional spacetimes, the results in [84![]() |
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7 | An early apparent success rested on a sign error [46]. Carter’s amended version of the proof was subject to a certain inequality between the electric and the gravitational potential [50]. | |
8 | As already mentioned in Section 5.4, these black holes present counter-examples to the naive generalization of the staticity theorem; they are nice illustrations of the correct non-Abelian version of the theorem [302, 303]. | |
9 | The symmetry condition (6.13![]() ![]() ![]() |
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10 | In addition to the actual scalar fields, the effective action comprises two gravitational scalars (the norm and the generalized twist potential) and two scalars for each stationary Abelian vector field (electric and magnetic potentials). | |
11 | A workable formula for ![]() ![]() |
http://www.livingreviews.org/lrr-2012-7 |
Living Rev. Relativity 15, (2012), 7
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