So, if all the null geodesics collide, there is no boundary to the future.
3.
We also have two sets of null geodesics spiralling into two different events on the green world line.
4.
It is worth remarking that the null geodesics " spiral " inwards in the above figure.
5.
One can define geometrical quantities that measure the Lorentz boost and area increase on going round these closed null geodesics.
6.
Roger Penrose has observed that near a null geodesic, " every Lorentzian spacetime looks like a plane wave ".
7.
In general relativity, it is assumed that inertial motion occurs along timelike and null geodesics of spacetime as parameterized by proper time.
8.
Expressing the metric in this form shows clearly that null geodesics are inclined at \ pm 45 ^ \ circ to the horizontal.
9.
When the null geodesics intersect, they are no longer on the boundary of the future, they are in the interior of the future.
10.
These families of inward and outward bound radial null geodesics represent very different curves in spacetime and their projections do not agree for ? > 0.
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