Contents

25.5 Einstein–Maxwell fields 401The conformally flat Bell–Szekeres solution is contained as the limit β =0,p =1. A second solution given in that paper provides a generalization ofthe Bell–Szekeres solution in the same way as the axisymmetric distortedstatic black-hole solutions are a generalization of the Schwarzschild solution.The discussion of these Einstein–Maxwell fields shows that horizonsform and timelike singularities develop.Another approach uses the generalization of the complex vacuum potentialZ = χ +iω defined in (25.7), which also satisfies the Ernst equation,to the Einstein–Maxwell case. This gives rise to another correspondencebetween stationary axisymmetric and colliding plane wave solutions. Asmentioned at the beginning of §25.4, the Kerr solution can be consideredas the counterpart of the Nutku–Halil solution. The Kerr–Newmansolution is then the analogue of a solution given by Chandrasekhar andXanthopoulos (1985a). In this paper the same procedure which leads fromKerr to Kerr–Newman was applied to the Nutku–Halil solution. For themetric functions in the line element (25.12) one getse N =Ω 2 ∆(1 − η 2 ) −1/4 (1 − µ 2 ) −1/4 , χ =Ω 2 ∆Σ −1 ,(25.57)ω = 1 2 qµ{(1+α)2 +(1−α) 2 p −2 [q 2 (1−µ 2 ) 2 +(3−µ 2 )Σ]}/α 2 Σ + const,where p 2 + q 2 =1,αis a real parameter restricted to the range 0 ≤ α ≤ 1,and the abbreviations∆=1− p 2 η 2 − q 2 µ 2 , Σ=(1− pη) 2 + q 2 µ 2 ,Ω 2 = α −2[ √2(1 − α)√1 − µ 2 1 − η Σ/∆+1+α] 2 (25.58)+ α −2 p −2 ∆ −2 [(1 − α)2q(1 − µ 2 )(1 − pη)] 2are used. For α = 1, this metric reduces to the Nutku–Halil solution(25.22) with (25.33). The solution that is obtained describes the collisionbetween two plane impulsive gravitational waves, each supporting anelectromagnetic shock wave.The method presented in Chandrasekhar and Xanthopoulos (1985a)has been applied to particular seed metrics by Halilsoy (1990b, 1993b).Papacostas and Xanthopoulos (1989) investigated the Petrov type DEinstein–Maxwell fieldds 2 =(t 2 + z 2 ) −1 [ E 2 (dy − z 2 dx) 2 + H 2 (dy + t 2 dx) 2]+(t 2 + z 2 )(dz 2 /H 2 − dt 2 /E 2 ), (25.59)E 2 = − 1 2 at2 + bt +c ,H 2 = − 1 2 az2 + mz + n