Dilaton test of connection between AdS_3 X S^3 and 5D black hole

TL;DR

This paper investigates the connection between 5D black holes and BTZ black holes in string theory by calculating and comparing the greybody factors of the dilaton, confirming their agreement in a specific approximation.

Contribution

It introduces a harmonic gauge to decouple the dilaton from other fields and demonstrates the agreement of greybody factors between 5D black holes and BTZ black holes in the dilute gas limit.

Findings

Greybody factors of the dilaton match between 5D black hole and BTZ black hole.

Harmonic gauge effectively decouples the dilaton in the analysis.

Agreement supports the connection between 5D black holes and AdS$_3$ geometries.

Abstract

A 5D black hole(M$_5$) is investigated in the type IIB superstring theory compactified on S$^1 \times $T$^4$. This corresponds to AdS$_3 \times $S$^3 \times $T$^4$ in the near horizon with asymptotically flat space. Here the harmonic gauge is introduced to decouple the mixing between the dilaton and others. On the other hand we obtain the BTZ balck hole(AdS$_3\times$S$^3\times$T$^4$) as the non-dilatonic solution. We calculate the greybody factor of the dilaton as a test scalar both for a 5D black hole(M$_5 \times $S$^1 \times $T$^4$) and the BTZ black hole(AdS$_3 \times $S$^3 \times $T$^4$). The result of the BTZ black hole agrees with the greybody factor of the dilaton in the dilute gas approximation of a 5D black hole.