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Weak Gravity Conjecture and extremal black holes

Abstract

Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4D. We use the entropy function formalism to extend previous analysis that dealt with neutral particles, and obtain the corrections to the horizon entropy for different regimes of black hole masses. These corrections are small in general. They are furthermore reduced when supersymmetry is present, and disappear in N = 4 supergravity. We provide some speculative arguments that in a theory with only sub-extremal particles, classical Reissner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer, as shown by the horizon entropy computation.

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Correspondence to Gary Shiu.

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Cottrell, W., Shiu, G. & Soler, P. Weak Gravity Conjecture and extremal black holes. Sci. China Phys. Mech. Astron. 62, 110412 (2019). https://doi.org/10.1007/s11433-019-9406-2

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Key words

  • black holes
  • string theory
  • entropy