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

Frederik Denef, Gregory W. Moore

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The BekensteinHawking 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.

Original languageEnglish (US)
Pages (from-to)679-684
Number of pages6
JournalInternational Journal of Modern Physics D
Issue number3-4
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Black holes
  • Entropy
  • Microstates

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