World Lines in General Relativity
The use of world lines in general relativity is basically the same as in special relativity, with the difference that spacetime can be curved. A metric exists and its dynamics are determined by the Einstein field equations and are dependent on the mass distribution in spacetime. Again the metric defines lightlike (null), spacelike and timelike curves. Also, in general relativity, world lines are timelike curves in spacetime, where timelike curves fall within the lightcone. However, a lightcone is not necessarily inclined at 45 degrees to the time axis. However, this is an artifact of the chosen coordinate system, and reflects the coordinate freedom (diffeomorphism invariance) of general relativity. Any timelike curve admits a comoving observer whose "time axis" corresponds to that curve, and, since no observer is privileged, we can always find a local coordinate system in which lightcones are inclined at 45 degrees to the time axis. See also for example Eddington-Finkelstein coordinates.
World lines of free-falling particles or objects (such as planets around the Sun or an astronaut in space) are called geodesics.
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