The following is an example of hartle :
Consider the two dimensional metric ds^2 = -X^2 dT^2 + dX^2 And the world line X(T)=A cosh(T) where A is a constant with the dimensions of length. The light cones are the curves with ds^2=0 that have slopes dT/dX = +-1/X
A particle's world line is time like if the size of its slope |dT/dX| is bigger than 1/X
Can somebody explain how writer claims that
- dT/dX should be +1/X and -1/X
- world line is time like if the size of its slope is bigger than 1/X