Title: Gravitational Waves of Second Order in Empty Space
Abstract: The gravitational waves of second order in empty space with any gravitational field are investigated theoretically by the method of characteristics. A ten-dimensional space \mathfrakT10 is introduced and the propagation condition is resolved in \mathfrakT10 representation. Three kinds of waves, transverse, longitudinal and shear, are derived formally. It is proved that real waves are transverse, and longitudinal and shear waves can be canceled out by appropriate coordinate transformations.