The fact that the null geodesics appear " bent " in this chart is of course an artifact of our choice of " comoving " coordinates in which the world lines of the dust particles appear as vertical coordinate lines.
32.
If a point is on the boundary of the boundaries of the region, it can only be reached by going at the speed of light, no slower, so null geodesics include the entire boundary of Yoda proper future of a region.
33.
Penrose concluded that whenever there is a cube where all the outgoing ( and ingoing ) light rays are initially converging, the boundary of the future of that region will end after a finite extension, because all the null geodesics will converge.
34.
This is computed by sending a null geodesic from the world line of our observer ( event A ) to the world line of some small object, whereupon it is reflected ( event B ) and returns to the observer ( event C ).
35.
A manifold " M " is asymptotically simple if it admits a conformal compactification \ tilde { M } such that every null geodesic in " M " has future and past endpoints on the boundary of \ tilde { M }.
36.
However, the physical interpretation in terms of test particles and tidal accelerations ( for timelike geodesic congruences ) or pencils of light rays ( for null geodesic congruences ) is valid only for general relativity ( similar interpretations may be valid in closely related theories ).
37.
However, integrating the Landau-Lifschitz arc length along the track of null geodesics does not in general agree with the corresponding radar distance " in the large " since we are adding up small time intervals belonging to ideal clocks carried by " distinct"
38.
Indeed, since every solution to the field equations of this theory is a spacetime which is among other things conformally equivalent to flat spacetime, null geodesics must agree with the null geodesics of the flat background, so " this theory can exhibit no light bending ".
39.
Indeed, since every solution to the field equations of this theory is a spacetime which is among other things conformally equivalent to flat spacetime, null geodesics must agree with the null geodesics of the flat background, so " this theory can exhibit no light bending ".
40.
In the curved spacetime formulation the motion of test particles is described ( the world line of a free test particle is a timelike geodesic, and by an obvious limit, the world line of a laser pulse is a null geodesic ), but we lose the conservation law.
