A new form of the C-metric

The usual form of the C-metric has the structure function G (ξ) = 1 − ξ 2 − 2 mA ξ 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 factorizable structure function G (ξ) = (1 − ξ 2 )(1 + 2 mA ξ). 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 − ξ 2 )(1 + r + A ξ)(1 + r − A ξ), 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.