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Arman777

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*Consider a semi-Riemannian manifold which of these statements is false:*

1) All vectors on the light-cone are light-like, all vectors in the interior of the light-cone are time-like and all vectors in the exterior of the light-cone are space-like.

2) All space-like vectors lie in the exterior of the light-cone, all time-like vectors lie in the interior of light-cone, and all light-like vectors lie on the light-cone.

I can't see which statements are false, any help would be appreciated.

1) All vectors on the light-cone are light-like, all vectors in the interior of the light-cone are time-like and all vectors in the exterior of the light-cone are space-like.

2) All space-like vectors lie in the exterior of the light-cone, all time-like vectors lie in the interior of light-cone, and all light-like vectors lie on the light-cone.

I can't see which statements are false, any help would be appreciated.

What you guys think ?

I think 2) is True because that's kind of the definition but the 1) seems odd. It seems like it is true but I couldn't think any counter-example for the condition. Any ideas ?

https://physics.stackexchange.com/q...ightlike-vectors-and-the-light-cone-structure