nepalnsa.blogg.se

* Penrose-Khan vacuum (a simple colliding plane wave model), * double Kerr vacuum (two Kerr objects sharing the same axis of rotation, but held apart by unphysical zero active mass "cables" going out to suspension points infinitely removed),

* Kerns/Wild vacuum (a Schwarzschild object immersed in an ambient "almost uniform" gravitational field), * Taub-NUT vacuum (a famous counterexample describing the exterior gravitational field of an isolated object with strange properties), * Kerr vacuum (which describes the geometry around a rotating object), * Schwarzschild vacuum (which describes the spacetime geometry around a spherical mass), Milne describing an empty universe which has no curvature) * Milne model (which is a model developed by E. * Minkowski spacetime (which describes empty space with no cosmological constant) Well known examples of explicit vacuum solutions include: This means that the gravitational field outside the Sun is a bit "stronger" according to general relativity than it is according to Newton's theory. The fact that the gravitational field itself possesses energy yields a way to understand the nonlinearity of the Einstein field equation: this gravitational field energy itself produces more gravity. However, determining the precise location of this gravitational field energy is technically problematical in general relativity, by its very nature of the clean separation into a universal gravitational interaction and "all the rest". But the gravitational field can do work, so we must expect the gravitational field itself to possess energy, and it does.

This follows from the fact that these two second rank tensors stand in a kind of dual relationship they are the trace reverse of each other:: G_ = 0 in a vacuum region, it might seem that according to general relativity, vacuum regions must contain no energy. It is a mathematical fact that the Einstein tensor vanishes if and only if the Ricci tensor vanishes. More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. According to the Einstein field equation, this means that the stress-energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.