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I have just read (in the black holes chapter 14 on p244 of this book Ref.1) that in string theory, when one adds an (electric?) charge $Q$ to a static black hole, one can arrive at an exotic supersymmetric black hole. This sentence is not explained further and there are several (I think related enough) things I dont understand about it, which can be summerized under the question what really is an exotic suppersymmetric black hole?

First, how exactly does the addition of a charge (if it is not outright a supercharge) lead to supersymmetry?

Second, what is meant by an exotic black hole, conversely to for example an extremal black hole that has just the maximum charge allowed given its mass?

Third, what does it mean for a black hole to be supersymmetric anyway?

References:

  1. D. McMohan, String Theory Demystified, McGraw-Hill, 2009
Qmechanic
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Dilaton
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A supersymmetric black hole is a black hole solution in supergravity that preserves some fraction of supersymmetry. This occurs when the solution satisfies a BPS bound, meaning the mass, charge, and angular momentum obey relations ensuring the cancellation of quantum corrections. These black holes are extremal $T_H = 0$ and stable against decay.

Adding charge to a black hole can lead to supersymmetry if the charge comes from a gauge field in a supersymmetric theory. In supergravity, certain charged extremal black holes satisfy the first order BPS equations, implying they preserve some Killing spinors and thus some supersymmetry.

An exotic black hole generally refers to solutions in string theory that differ from classical Kerr-Newman or Reissner-Nordström black holes. These can include black holes with extra charges (e.g., from Kalb-Ramond fields), higher-dimensional effects, or configurations coming from D-branes.

Suraj Gavhale
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