Extremal single-charge small black holes: Entropy function analysis

TL;DR

This paper analyzes the entropy of extremal small black holes with D0-brane charge in type IIA string theory using Sen's entropy function formalism, revealing a rac12;rac12; charge dependence and conditions for solution existence.

Contribution

It demonstrates that the entropy scales as rac12;rac12;|q| for large charge and proves the force on a probe D0-brane must vanish for solutions to exist, consistent across higher derivative corrections.

Findings

Entropy scales as rac12;rac12;|q| for large charge

Force on probe D0-brane must vanish for solutions

Sub-leading corrections and duality relations discussed

Abstract

We study stretched horizons of the type AdS_2 x S^8 for certain spherically symmetric extremal small black holes in type IIA carrying only D0-brane charge making use of Sen's entropy function formalism for higher derivative gravity. A scaling argument is given to show that the entropy of this class of black holes for large charge behaves as \sqrt{|q|} where q is the electric charge. The leading order result arises from IIA string loop corrections. We find that for solutions to exist the force on a probe D0-brane has to vanish and we prove that this feature persists to all higher derivative orders. We comment on the nature of the extremum of these solutions and on the sub-leading corrections to the entropy. The entropy of other small black holes related by dualities to our case is also discussed.