Introduction

Do Einstein's equations permit the existence of gravitational waves? As in the case of electromagnetism, where Maxwell's field equations led to the important deduction of electromagnetic waves carrying energy and momentum with the speed of light, one expects the relativistic equations to imply the existence of gravitational waves that do the same. However, several issues intervene to make the answer to our question nontrivial.

The first problem is posed by the non-linearity of the Einstein field equations. In the wave motion discussed in electromagnetic theory, acoustics, elastic media, etc. the basic equations are linear and a superposition principle holds. There is no corresponding situation in general relativity. Secondly, there is no corresponding vector or tensor in relativity that plays the role of the Poynting vector in the transport of electromagnetic energy.

A third difficulty arises from the general covariance of the field equations. With the facility available to use any coordinate system as per convenience, it is not clear whether a particular ‘wavelike’ solution is a real physical effect or a pure coordinate effect. Thus one has to be on guard against solutions that describe coordinate waves that may travel ‘with the speed of thought’.

Even during Einstein's lifetime, the above question did not receive an unequivocal answer.