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Posted by pmb on February 24, 2000 13:18:18 UTC

One has to be careful when using the term "mass" when speaking about light. The gravitational field created by light is (while more complicated than a particle) produces twice the acceleration on particles that would normally be expected from m = E/c2. Light, when acting as a source of gravity, is said to posses an active gravitational mass (i.e. the mass that acts like the source of gravity). When light is responding to gravity then that property is called the passive gravitational mass.

The statement In GR mass almost always means the m in : m2c2 = gmnPmPn. is incorrect. If the mass refers to the source and is not otherwise qualified then they mean mass-energy (i.e. integral of T00) [See the definition for "M" in MTW page 452 Eq. 19.14]. If the mass refers to the mass of an object moving in the field then they mean rest mass (however they usually quality it at least once).

re = Otherwise for extended bodies, "system mass" is useless. - Not if it's the source of gravity. - MTW page 452.

re - If we restrict ourselves to using ordinary three component vectors in a SR revision of Newtonian mechanics it turns out the equation F = ma doesn't hold true anymore. ---

See --"Gravitational Force

re - Instead gravity is the tendency for particle to follow geodesics in curved space and time. - A region of spacetime need not be curved for there to be a gravitational field there. Curvature means the non-vanishing of the curvature tensor. However the equation of motion of a particle in a gravitational field, the geodesic equation, involves the metric (from which the Christoffel symbols are derived). Thus whether a particle is accelerating relative the the source of gravity or not is dependant, not on the curvature tensor, but on the metric tensor. Thus one can speak of a gravitational field with no curvature. A uniform gravitational field is an example. Part of the the definition of such a field is that the curvature tensor vanish. The metric is then derived from this and other defining characteristics.

For this reason the metric guv is called the gravitational field (actually the collection of all the 10 of the inependant components of guv).

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