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340 21 Non-empty stationary axisymmetric solutionsby Mars and Senovilla (1996). The line element has the form[ds 2 = N −2 (z) dz 2 +dx2 hm + s2+hm + s2 mdϕ2 − m(dt + s ) ] 2m dϕ ,N ′′ = εN, ε =0, ±1, Ω=−m ′′ /s ′′ , (21.74a)κ 0 µ = κ 0 p − 6(N ′2 − εN 2 ),κ 0 (µ + p) =N 2 (z)(h ′ m ′ + s ′2 +4ε)/2,where the three functions h(x), m(x) and s(x) have to satisfy the twodifferential equationsh ′′ m ′′ + s ′′2 =0, (hm + s 2 ) ′′ +4ε = h ′ m ′ + s ′2 . (21.74b)This class admits a conformal Killing vector ζ = ∂ z , cp. Mars and Senovilla(1994), and contains the rigidly rotating solutions (21.61) as thespecial case s ′′ =0=m ′′ . Only very special explicit solutions of (21.74)are known, where h, m and s are either powers of x (García D. 1994) ora product of powers of x with (x√1/10+ αx −√1/10 ) (Senovilla 1992).