It turns out that the most general pp-wave spacetime has only one Killing vector field, the null geodesic congruence k = \ partial _ v.
12.
He showed that some or all of the null geodesics emitted at a given event will be refocused at a later event ( or string of events ).
13.
Describing the mutual motion of the test particles in a null geodesic congruence in a spacetime such as the FRW dust is a very important problem in general relativity.
14.
:: My question might be better summed up by asking if each for each null geodesic will be there a light ray in the pulse that will follow it?
15.
Considering the null geodesic equation again, one can see that if dU / dt = c, dX / dt = 0 meaning that light comes to a standstill.
16.
Because of the simple character of null geodesics in Minkowski spacetime, we can readily determine the optical distance between our pair of Rindler observers ( aligned with the direction of acceleration ).
17.
(In Minkowski spacetime, fortunately, we can ignore the possibility of multiple null geodesic paths between two world lines, but in cosmological models and other applications things are not so simple!
18.
If the Cauchy surface were compact, i . e . space is compact, the null geodesic generators of the boundary can intersect everywhere because they can intersect on the other side of space.
19.
To show this, he used techniques imported from algebraic geometry to " blow up " the spacetime so that the given null geodesic becomes the covariantly constant null geodesic congruence of a plane wave.
20.
To show this, he used techniques imported from algebraic geometry to " blow up " the spacetime so that the given null geodesic becomes the covariantly constant null geodesic congruence of a plane wave.
