There is a connection between the origin and the points in the light cone.That is to say,there is a casual relationship between them.I think normal light cone means light which travels to the right side and to the left side have the same speed.Then in certain spacetime,eg. at the point of strong...
Smaller,but Larger??
You may have a look at the attachments,which are the key parts of my problem.
And the full text is here:http://arxiv.org/pdf/gr-qc/9905084v5.pdf
How to understand "The outermost surface of the warp bubble will have an area corresponding to a radius of approximately...
If the notions of covariant and contravariant tensors were not introduced,what would happen?E.g. what form will the Einstein E.q. Guv=8πTuv be changed into ?
Oh,sorry,I focused my attention to how to explain the unitarity(normalization) condition and forgot to check it...spacelike vector is not a good example.By the way,do u think spacelike vector and closed timelike curves could exist in nature (in reality)?
I just want this equation to be the unitarity(normalization) condition.E.g. Uu=(1,2,0,0) and (C,2C,0,0) are different in mathematics,but they have the similar physical meaning.So in order to make work easy,we use (1,2,0,0) to represent (C,2C,0,0)
Yeah,I agree the observer should measure it locally and so on,but I'm afraid this generalization is a matter of unitarity.e.g.guvUuUv=+/-1.I think another generalization is Uu=(1,a,0,0),that is to say,orthogonality or diagonal metric is not needed...In that case,ρ is not necessarily equal to T00...
The observer and the object has the same four-velocity U^u as (1,0,0,0),which means they are relatively static.Then the the observer measures a point A of the object's energy density,which is ρ.
My question is,the ρ is T^00 or T_00 at the point A?