Note on small black holes in AdSp × Sq

Abstract

It is commonly believed that small black holes in AdS5 × S5 can be described by the ten dimensional Schwarzschild solution. This requires that the self-dual five-form (which is non-zero in the background) does not fall through the horizon and cause the black hole to grow. We verify that this is indeed the case: there are static solution to the five-form field equations in a ten dimensional Schwarzschild spacetime. Similar results hold for other backgrounds AdSp × Sq of interest in supergravity.