This chapter considers the vacuum solution that was referred to as the C-metric in the classic review of Ehlers and Kundt (1962) – a label that has generally been used ever since. In fact, the static form of this solution was originally found by Levi-Civita (1918) and Weyl (1919a), and has subsequently been rediscovered many times. Its basic properties were first interpreted by Kinnersley and Walker (1970) and Bonnor (1983). Specifi- cally, it was shown that, with its analytic extension, this solution describes a pair of causally separated black holes which accelerate away from each other due to the presence of strings or struts that are represented by conical singularities.

The C-metric is a generalisation of the Schwarzschild solution which includes an additional parameter that is related to the acceleration of the black holes. In fact, generalisations to “accelerating” versions of all three A-metrics have been described by Ishikawa and Miyashita (1983). These include what may be called the CI, CII and CIII-metrics. However, it is only the CI-metric, which describes accelerating black holes, that will be considered in the present chapter.

General properties of space-times such as this, which admit boost and rotationsymmetries, were described by Bičák (1968). Asymptotic and other properties of the C-metric were further investigated by Farhoosh and Zimmerman (1980a), Ashtekar and Dray (1981), Dray (1982), Bičák (1985) and Cornish and Uttley (1995a). For more recent work see e.g. Pravda and Pravdová (2000) and Griffiths, Krtouš and Podolsky (2006), on which the present chapter is based and from where the figures are taken.