The positive mass theorem for multiple rotating charged black holes. (English) Zbl 1339.83029
Summary: In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by P. T. Chruściel and J. L. Costa [Classical Quantum Gravity 26, No. 23, Article ID 235013, 7 p. (2009; Zbl 1181.83015)] to the case of multiple black holes. We also weaken the hypotheses used in the proof of this result for single black holes, and establish the associated rigidity statement.
MSC:
| 83C22 | Einstein-Maxwell equations |
| 83C57 | Black holes |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 35Q75 | PDEs in connection with relativity and gravitational theory |
Keywords:
positive mass theorem; multiple rotating charged black holes; ADM mass; axisymmetric initial data sets; Einstein-Maxwell equations; rigidity statementCitations:
Zbl 1181.83015References:
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