Sanford Posted April 11, 2010 Share Posted April 11, 2010 Someone emailed me the following statement that does not make sense to me. "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone." Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish? Link to comment Share on other sites More sharing options...
ajb Posted April 12, 2010 Share Posted April 12, 2010 The field equations are clearly non-linear in the metric. This leads to technical difficulties in dealing with gravity but also is the origin of gravitational self-interactions. Think of point charges in electromagnetic theory. The charge is isolated at a point but the electromagnetic field is non-trivial around the charge. The same thing happens in general relativity. The energy-momentum acts as a source of gravity. This does not mean that where we have no energy-momentum the geometry is necessarily trivial (flat). The so called vacuum field equations reduce to the statement that the space-time is Ricci flat. ([math]R_{\mu \nu}=0 [/math] ). This does not mean that the Riemann curvature is zero. In fact I am sure you know of several vacuum solutions, that is no energy-momentum on the RHS of the field equations. For example the Schwarzschild solution is one well-known example. Link to comment Share on other sites More sharing options...
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