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We investigate the ultrarelativistic boost of a Schwarzschild black holeimmersed in an external electromagnetic field, described by an exact solutionof the Einstein-Maxwell equations found by Ernst (the ``Schwarzschild-Melvin''metric). Following the classical method of Aichelburg and Sexl, thegravitational field generated by a black hole moving ``with the speed oflight'' and the transformed electromagnetic field are determined. Thecorresponding exact solution describes an impulsive gravitational wavepropagating in the static, cylindrically symmetric, electrovac universe ofMelvin, and for a vanishing electromagnetic field it reduces to the well knownAichelburg-Sexl pp-wave. In the boosting process, the original Petrov type I ofthe Schwarzschild-Melvin solution simplifies to the type II on the impulse, andto the type D elsewhere. The geometry of the wave front is studied, inparticular its non-constant Gauss curvature. In addition, a more general classof impulsive waves in the Melvin universe is constructed by means of asix-dimensional embedding formalism adapted to the background. A coordinatesystem is also presented in which all the impulsive metrics take a continuousform. Finally, it is shown that these solutions are a limiting case of a familyof exact gravitational waves with an arbitrary profile. This family isidentified with a solution previously found by Garfinkle and Melvin. We thuscomplement their analysis, in particular demonstrating that such spacetimes areof type II and belong to the Kundt class.Comment: 11 pages, REVTeX

Ultrarelativistic black hole in an external electromagnetic field and gravitational waves in the Melvin universe