Note on Small Black Holes in AdS_p x S^q

TL;DR

This paper investigates the existence of static five-form field solutions in ten-dimensional Schwarzschild spacetimes, supporting the idea that small black holes in AdS_5 x S^5 can be modeled by such solutions without growth due to the five-form.

Contribution

It demonstrates the existence of static five-form solutions in Schwarzschild backgrounds, confirming assumptions about small black holes in AdS x S backgrounds.

Findings

Static five-form solutions exist in ten-dimensional Schwarzschild spacetime.

Similar solutions are found in other AdS_p x S^q backgrounds.

Supports the modeling of small black holes in AdS with these solutions.

Abstract

It is commonly believed that small black holes in AdS_5 x S^5 can be described by the ten dimensional Schwarzschild solution. This requires that the self-dual five-form (which is nonzero 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 solutions to the five-form field equations in a ten dimensional Schwarzschild spacetime. Similar results hold for other backgrounds AdS_p x S^q of interest in supergravity.