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Matrix norms, BPS bounds and marginal stability in \(\mathcal{N} = 8\) supergravity. (English) Zbl 1294.83049

Summary: We study the conditions of marginal stability for two-center extremal black holes in \(\mathcal{N} \)-extended supergravity in four dimensions, with particular emphasis on the \(\mathcal{N} = 8\) case.{ }This is achieved by exploiting triangle inequalities satisfied by matrix norms. Using different norms and relative bounds among them, we establish the existence of marginal stability and split attractor flows both for BPS and some non-BPS solutions.{ }Our results are in agreement with previous analysis based on explicit construction of multi-center solutions.

MSC:

83C57 Black holes
83E30 String and superstring theories in gravitational theory
83E50 Supergravity
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
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