Gravitational plane wave
In general relativity, a gravitational plane wave is a special class of a vacuum pp-wave spacetime, and may be defined in terms of Brinkmann coordinates by
Here, can be any smooth functions; they control the waveform of the two possible polarization modes of gravitational radiation. In this context, these two modes are usually called the plus mode and cross mode, respectively.
Gravitational waves exist and travel at the speed of light. Every form of matter and energy with which we are familiar has the same gravitational effect positive attraction. Gravitational waves are very weak. Consider two neutron stars of one solar mass and radius rNS = 6 km orbiting each other essentially in contact.
The characteristic acceleration at the neutron stars is
