Black Holes and Naked Singularities in an Infinite Momentum Frame

Abstract

The problem of the construction of shock waves by the boosting method for metrics of black holes and naked singularities is considered. It is noted that singular terms may arise under the boosting, which prevents the generation of shock waves (in particular, in the case of the absence of quasi-Cartesian coordinates). We find that if the Fisher metric of a black hole with a scalar charge and a singular horizon is boosted, then the scalar field disappears (unlike the case of black holes with electric and magnetic charges). It is noted that boosted metrics are solutions of the linearized Einstein equations, while the original metrics are exact nonlinear solutions of these equations. The event horizon disappears under the boosting. Thus, the boosting of naked singularities leads to the same result as the boosting of black holes. This is confirmed by the example of gamma-metrics (Zipoy–Vourhees solution) as well. Finally, it is shown that if a linearized metric is boosted with the Newman–Unti–Tamburino parameter (NUT) along the Misner string, then a shock wave with a nondiagonal structure of the gyraton is obtained.