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

Annals of Physics

Volumn 282, Issue 1, 2000, Pages 115-137

  Cooperstock, F I ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008049995     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1006/aphy.2000.6032     Document Type: Article

References (29)

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13. In the strictest sense, one might argue that this does not provide adequate grounds to refer to this as a necesssary condition for mass loss as one might imagine the stress-trace part of the Tolman integral first increases, as we have shown, and later reverses its course and either stays constant or diminishes at a later stage to yield a net mass loss. While there would not appear to be any basis for expecting such a qualitative shift in behaviour, it cannot be ruled out completely in the absence of a calculation to complete the cycle. Moreover, it should be noted that traditional previous calculations make similar assumptions that start-up and wind-down effects will not alter the essential conclusions.
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20. Note that for stationary systems, the energy of a system can be calculated from the volume integral in (6), and by comparison with (15), the Tolman stress integral can be viewed as embodying the essence of the gravitational contribution to energy. To ignore its role in the context of, gravitational, energy loss computations is particularly illogical.
21. Many years ago, the late J. L. Synge related to the author how Eddington responded to criticism of some of his mathematical techniques: "I don't care what they say - I can feel it in my bones!" One can only marvel at the power of Eddington's skeletal receptors.
22. It should be noted that the raising and subsequent lowering of indices in the following sequence is required, first because the substitution proceeds with raised indices whereas the initial equation has mixed indices and second, because the final Tolman expression demands mixed indices so we must revert in the end. In Einstein's derivation, this was trivial because at the lower order, the raising and lowering was adequately performed with the Minkowski metric.
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29. 2, is not constant. This is seen from a calculation of the rate of change of the matter part of the angular momentum (to be published). This result, in conjunction with (8), determines the rate of increase of the moment of inertia of the rod, and its third time derivative is the first term on the RHS of (27). We find that this term is of too high an order to be of interest.