A new form of the C-metric

Details A new form of the C-metric A new form of the C-metric

2003-05-23

arxiv.org/abs/gr-qc/0305089v2

Class.Quant.Grav. 20 (2003) 3269-3277

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 1 LaTeX figure; references added

Scientific paper

10.1088/0264-9381/20/14/321

The usual form of the C-metric has the structure function G(\xi)=1-\xi^2-2mA\xi^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(\xi)=(1-\xi^2)(1+2mA\xi). 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(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), 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.

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