Abstract
Three subclasses of stationary axially symmetric diagonal Weyl metrics satisfying the empty-space Einstein equations are presented in an explicit form. These solutions generalize the $C$ metric (mass with constant acceleration) and contain six free parameters. Four of these parameters appear as exponents playing a role similar to $\ensuremath{\delta}$ in the Tomimatsu-Sato solution (mass with quadrupole moment). For integer values of the exponents these metrics are constructed from rational functions only. Special cases include various metrics of physical interest.
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