A new form of the C-metric

Abstract

The usual form of the C-metric has the structure function G(ξ)=1-ξ^2-2mAξ^3, 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 factorisable structure function G(ξ)=(1-ξ^2)(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 the new form G(ξ)=(1-ξ^2)(1+r_{+}Aξ)(1+r_{-}Aξ), where r_{\pm} are the usual locations of the horizons in the Reissner-Nordstrom solution. As a by-product, we explicitly cast the extremally charged C-metric in Weyl coordinates.