Free-Field Realization of D-dimensional Cylindrical Gravitational Waves

TL;DR

This paper develops a free-field formulation for D-dimensional gravitational waves with symmetries, enabling a simplified analysis of their structure and metric components through canonical transformations and asymptotic series.

Contribution

It introduces a novel free-field representation for D-dimensional gravitational waves with symmetries, linking dilaton gravity to free fields via canonical transformations.

Findings

Canonical transformation maps dilaton gravity to free fields

Spacetime metric components expressed as asymptotic series

Provides a framework for analyzing D-dimensional gravitational waves

Abstract

We find two-dimensional free-field variables for D-dimensional general relativity on spacetimes with D-2 commuting spacelike Killing vector fields and non-compact spatial sections for D>4. We show that there is a canonical transformation which maps the corresponding two-dimensional dilaton gravity theory into a two-dimensional diffeomorphism invariant theory of the free-field variables. We also show that the spacetime metric components can be expressed as asymptotic series in negative powers of the dilaton, with coefficients which can be determined in terms of the free fields.