Main Question or Discussion Point
What is the physical/geometric meaning of spacelike, timelike and null geodesics?
All objects with mass move on timelike geodesics, massless objects move on null geodesics, and nothing can move on spacelike geodesics since that would mean moving faster than the speed of light.What is the physical/geometric meaning of spacelike, timelike and null geodesics?
Locally, they are usually known as "straight lines".So what then is the practical relevance of spacelike geodesics to general relativity?
They have no physical usage in any branch of physics but in the FTL theories which lean upon a premise that says there are particles that can be accelerated in such a way that their speed would be able to pass the speed of light! An example could be tachyons. The reason why such particles follow spacelike geodesics is that since they have tremendously ultra-higher speeds than [tex]c[/tex], so an interval in space is travelled by them in a very tiny interval of time, letting the line-element [tex]ds^2[/tex] be smaller than zero.So what then is the practical relevance of spacelike geodesics to general relativity?