A new form of the C-metric

The usual form of the C-metric has the structure function G((zeta)) = 1 (zeta)^2 - 2mA(zeta)^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((zeta)) = (1 - (zeta)^2)(1 + 2mA(zeta)). 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((zeta)) = (1 - (zeta)^2)(1 + r+A(zeta))(1 + r-A(zeta)), where r+- 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.