The Energy-Momentum Tensor in General Relativity and in Alternative Theories of Gravitation, and the Gravitational vs. Inertial Mass

Details The Energy-Momentum Tensor in General Relativity and in Alternative Theories of Gravitation, and the Gravitational vs. Inertial Mass The Energy-Momentum Tensor in General Relativity and in Alternative Theories of Gravitation, and the Gravitational vs. Inertial Mass

2010-10-27

arxiv.org/abs/1010.5557v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Due to a glitch in the PDF conversion, the script letter representing the complete canonical energy-momentum tensor [Eq. (15)

Scientific paper

We establish a general relation between the canonical energy-momentum tensor and the tensor that acts as the source of the gravitational field in Einstein's equations. In General Relativity, we use this relation to give a general proof of the exact equality of the gravitational and inertial masses for any arbitrary system of matter and gravitational fields, regardless of the presence of nonminimal couplings. In the Brans-Dicke scalar field theory, we establish that the nonminimal coupling of the scalar field leads to an inequality between the gravitational and inertial masses, and we derive an exact formula for this inequality and confirm that it is approximately proportional to the gravitational self-energy (the Nordvedt effect), but with a constant of proportionality different from what is claimed in the published literature in calculations based on the PPN scheme. Similar inequalities of gravitational and inertial masses are expected to occur in other scalar and vector theories.

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