The Role of Energy and a New Approach to Gravitational Waves in General Relativity

The energy localization hypothesis of the author that energy is localized in non-vanishing regions of the energy-momentum tensor implies that gravitational waves do not carry energy in vacuum. If substantiated, this has significant implications for current research. Support for the hypothesis is provided by a re-examination of Eddington's classic calculation of energy loss by a spinning rod. It is emphasized that Eddington did not monitor the entire Tolman energy integral, concentrating solely upon the change of the 'kinetic' part of the energy . The 'quadrupole formula' is thus seen to measure the kinetic energy change. When the derivative of the missing stress-trace integral is computed, it is seen to cancel the Eddington term and hence the energy of the rod is conserved, in support of the localization hypothesis. The issue of initial and final states is addressed.