Self-interaction of gravitational waves and their observability

Abstract

Energy is not a well-defined concept in General Relativity (GR). There have been various approaches adopted, including simply discarding the concept. However, with mass-energy equivalence and the importance of mass in GR, many have thought it worth preserving. Of the various suggestions for defining energy, there is a proposal that the energy content in a time varying spacetime can be obtained by considering its second approximate Lie symmetries. Unlike others, this proposal allows one to calculate the energy in gravitational waves. When applied to cylindrical gravitational waves, it gives a self-damping of the waves. Though other waves may be expected to have different mathematical behaviour, the physics of self-damping should remain the same and one would expect a qualitatively similar result, even if it is quantitatively different in some details. If this proposal is valid, the estimates for the required sensitivity of the detectors for the various sources will have to be revised upwards. This revision is worked out here. In view of the fact that after two years of being online no signal has been seen by the detectors, it is argued that this proposal should be taken as a serious contender for a valid definition of energy in GR.