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Within general relativity (GR), Einstein's … Within general relativity (GR), Einstein's relativistic gravity, the gravitational field is described by the 10-component metric tensor. However, in Newtonian gravity, which is a limit of GR, the gravitational field is described by a single component Newtonian gravitational potential. This raises the question to identify the Newtonian potential within the metric, and to identify the physical interpretation of the remaining 9 fields. The definition of the non-relativistic gravitational fields provides the answer to this question, and thereby describes the image of the metric tensor in Newtonian physics. These fields are not strictly non-relativistic. Rather, they apply to the non-relativistic (or post-Newtonian) limit of GR. A reader who is familiar with electromagnetism (EM) will benefit from the following analogy. In EM, one is familiar with the electrostatic potential and the magnetic vector potential . Together, they combine into the 4-vector potential , which is compatible with relativity. This relation can be thought to represent the non-relativistic decomposition of the electromagnetic 4-vector potential. Indeed, a system of point-particle charges moving slowly with respect to the speed of light may be studied in an expansion in , where is a typical velocity and is the speed of light. This expansion is known as the . Within this expansion, contributes to the two-body potential already at 0th order, while contributes only from the 1st order and onward, since it couples to electric currents and hence the associated potential is proportional to . associated potential is proportional to .
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| rdfs:comment |
Within general relativity (GR), Einstein's … Within general relativity (GR), Einstein's relativistic gravity, the gravitational field is described by the 10-component metric tensor. However, in Newtonian gravity, which is a limit of GR, the gravitational field is described by a single component Newtonian gravitational potential. This raises the question to identify the Newtonian potential within the metric, and to identify the physical interpretation of the remaining 9 fields. interpretation of the remaining 9 fields.
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Non-relativistic gravitational fields
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