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Smooth extremal horizons are the exception, not the rule
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We show that the general charged, rotating black hole in five-dimensional Einstein-Maxwell theory has a singular extremal limit. Only the known analytic solutions with exactly zero charge or zero angular momenta have smooth extremal horizons. We also consider general black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory, and show that they also have singular extremal limits except for one special value of the coefficient of the Chern-Simons term (the one fixed by supergravity). Combining this with earlier results showing that extremal black holes have singular horizons in four-dimensional general relativity with small higher derivative corrections, and in anti-de Sitter space with perturbed boundary conditions, one sees that smooth extremal horizons are indeed the exception and not the rule.
Forward citations
Cited by 3 Pith papers
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Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity
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Charged and rotating near-horizon geometries in five dimensions
New closed-form charged rotating five-dimensional near-horizon geometries exist with two independent angular momenta and constant co-rotating electric field, characterized by Sasakian structure and matching expected e...
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Instability of Black Holes in AdS$_3 \times S^3$
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