General Relativity and Gravitation

, Volume 39, Issue 10, pp 1539–1544

How many black holes fit on the head of a pin?

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DOI: 10.1007/s10714-007-0469-4

Cite this article as:
Denef, F. & Moore, G.W. Gen Relativ Gravit (2007) 39: 1539. doi:10.1007/s10714-007-0469-4


The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations.

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Instituut voor Theoretische FysicaKU LeuvenLeuvenBelgium
  2. 2.NHETC and Department of Physics and AstronomyRutgers UniversityPiscatawayUSA