Approximate Stress Energy Tensor for Gravitational Fields

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Abstract
An invariant formulation in Minkowski space‐time of an approximation to the Einstein theory of gravitation is given. In this formulation a tensor is introduced which may be interpreted as the approximate stress energy tensor of the gravitational field. Conservation laws involving this tensor and the material stress energy tensor are formulated. The behavior of these tensors under ``gauge transformations'' of the weak gravitational fields is discussed. The classical limit of the conservation of energy equation is studied and the results are compared to some observations of Bondi on a possible analog of the Poynting vector for a gravitational field.

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