Non-Parallel Electric and Magnetic Fields in a Gravitational Background, Stationary Gravitational Waves and Gravitons

The existence of an electromagnetic field with parallel electric and magnetic field components in the presence of a gravitational field is considered. A non-parallel solution is shown to exist. Next, we analyse the possibility of finding stationary gravitational waves in nature. Finally, we construct a D=4 effective quantum gravity model. Tree-level unitarity is verified.