Gravitational plane wave
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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 should exist and travel with speed of light which is the only Lorentz invariant velocity and is the relation between space and time. 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 (MNS =M) and radius rNS = 6 km orbiting each other essentially in contact. (This is for example, clearly tidal forces will have a very disruptive effect on the two neutron stars.)
The characteristic acceleration at the neutron stars is
- Problem Set 12: GRAVITATIONAL WAVES G. F. SMOOT Department of Physics, University of California, Berkeley, USA 94720