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.
Read more about this topic: World Line
Famous quotes containing the words world, lines, general and/or relativity:
“I have learned more about love, selflessness and human understanding in this great adventure in the world of AIDS than I ever did in the cut-throat, competitive world in which I spent my life.”
—Anthony Perkins (1932–1992)
“Your letter is come; it came indeed twelve lines ago, but I
could not stop to acknowledge it before, & I am glad it did not
arrive till I had completed my first sentence, because the
sentence had been made since yesterday, & I think forms a very
good beginning.”
—Jane Austen (1775–1817)
“If men would avoid that general language and general manner in which they strive to hide all that is peculiar and would say only what was uppermost in their own minds after their own individual manner, every man would be interesting.”
—Ralph Waldo Emerson (1803–1882)
“By an application of the theory of relativity to the taste of readers, to-day in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!”
—Albert Einstein (1879–1955)