Abstract. The usual form of the C-metric has the structure function G(ξ) = 1 − ξ² − 2mAξ³, whose cubic nature can make calculations cumbersome, especially when explicit expressions for its roots are required. In this paper, we propose a new form of the C-metric, with the explicitly factorizable structure function G(ξ) = (1 − ξ²)(1 + 2mAξ). Although this form is related to the usual one by a coordinate transformation, it has the advantage that its roots are now trivial to write down. We show that this leads to potential simplifications, for example, when casting the C-metric in Weyl coordinates. These results also extend to the charged C-metric, whose structure function can be written in a new form G(ξ) = (1 − ξ²)(1 + r₊Aξ)(1 + r₋Aξ), where r_± are the usual locations of the horizons in the Reissner–Nordström solution. As a by-product, we explicitly cast the extremally charged C-metric in Weyl coordinates.

PACS number: 04.20.Jb

Print publication: Issue 14 (21 July 2003)
Received 29 April 2003
Published 1 July 2003