Moduli space metric for maximally-charged dilaton black holes

TL;DR

This paper derives the moduli space metric for maximally-charged dilaton black holes, revealing the nature of their interactions and scattering behavior in string theory, with implications for understanding black hole dynamics.

Contribution

It provides the first explicit form of the moduli space metric for these black holes and clarifies the conditions under which many-body interactions occur.

Findings

Only two-body interactions exist in string theory for these black holes.

Interaction vanishes if the dilaton is a Kaluza-Klein scalar.

Many-body interactions are present for general dilaton couplings.

Abstract

The system consisting of slowly-moving, maximally charged, nonrotating dilaton black holes is investigated. We obtain the metric on the moduli space of the system in the low-velocity limit. We find that: (1) only two-body interactions exist between the extreme black holes in string theory; (2) the mutual interaction between the black holes vanishes if the dilaton can be interpreted as a Kaluza-Klein scalar; and (3) for general dilaton couplings, there exist many-body interactions among the extreme black holes. We analyze the low-energy classical scattering of the two extreme black holes in string theory by utilizing the moduli space metric.