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17.3 Group G 1 on non-null orbits 271a finite region of space for all times. Consequently, the solution (17.20)cannot serve as a model describing the emission of gravitational wavesfrom an isolated source. Nevertheless, the Bonnor−Swaminarayan solutionis radiative.Similarly, the C-metric (§18.6) can be interpreted as the field of twoblack holes uniformly accelerated in opposite directions (Kinnersley andWalker 1970). Bonnor (1983) transformed the line element given for theC-metric in Table 18.2 into Weyl’s form (17.24), extended the manifoldand arrived at the interpretation of the gravitational field of two particlesuniformly accelerated by a spring between them. Cornish and Uttley(1995) presented a simplified version of Bonnor’s approach. There isa close analogy of the C-metric with the Born solution for acceleratedcharges in electrodynamics.Ernst (1978b) applied his procedure summarized by (20.21), (20.22) toderive the generalized C-metricds 2 = r 2 [ e λ(F +G) exp(−λ 2 r 4 AB)(dx 2 /A +dy 2 /B)+e λ(G−F ) Adz 2− e λ(F −G) Bdt 2] , F = Ar 2 + mx, G = Br 2 + my, (17.26)A =1− x 2 − mx 3 , B = y 2 − my 3 − 1, r =(x + y) −1 ,λ,m= const.In this boost-rotation-symmetric solution the nodal singularity of the originalC-metric can be eliminated by an appropriate choice of the additionalparameter λ which is related to the external gravitational field that causesthe acceleration of the particles (Dray and Walker 1980).It can be shown (Valiente Kroon 2000) that all the solutions in §29.2.6are boost-rotation-symmetric as the asymptotic form of at least two oftheir Killing vectors is the same as those of the C-metric.Bičák and Pravda (1999) investigated some properties of the twistinggeneralization of the C-metric which can be interpreted as a radiativespace-time with accelerating and rotating black holes.17.3 Group G 1 on non-null orbitsStationary gravitational fields (Chapter 18) admit a timelike Killing vector.The reduction formulae for the Ricci tensor derived in §18.2 for atimelike Killing vector also hold in the case of a spacelike Killing vector.For vacuum and some restricted classes of perfect fluids, the generationprocedure outlined in §10.3.2 can be used to obtain a one-parameter familyof solutions from any seed solution admitting a G 1 , see e.g. Garfinkleet al. (1997) for applications.