# Frame of reference

1. Aug 24, 2004

### eljose79

given a frame of reference s In General Relativity in wich you meassure an interval of space dx, could we have another frame Sso the observer in that Ssee that dx observed in S as a time interval dt?

2. Aug 24, 2004

### robphy

If you are asking
"Could [in a small neighborhood] a displacement interval be determined to be spacelike (i.e., have negative square-norm) to one observer but timelike (i.e., have positive square-norm) to another observer?",
the answer is no.
The character of the displacement interval is determined by the metric tensor at the event, not by the choice an observer at that event.

3. Aug 24, 2004

### pervect

Staff Emeritus
I don't think so. A spacelike interval will remain spacelike for all observers, a timlike interval will remain timelike.

4. Aug 25, 2004

### LURCH

In anither thread (about Black Holes) somone mentioned reading that, at the EH, spacelike worldlines become timelike and vise-versa. Is this incorrect?

5. Aug 25, 2004

### selfAdjoint

Staff Emeritus
In the Schwartzschild metric, the "radial" direction out side the horizon switches to a time direction inside. This again is a feature of that coordinate system.

6. Aug 25, 2004

### pervect

Staff Emeritus
No, it is correct that at the event horizon the 'r' coordinate switches roles from being space-like to time-like. However, the original question was whether some specific interval could be considered space-like by one observer, and time-like by another. The fact that the r-coordiante is time-like inside the event horizon and space-like outside does not imply that different observers see the same interval differently. _All_ observers will agree that some vector pointing in the 'r' direction is spacelike when r is outside the event horizon. And they'll agree that a different vector r1 located inside the event horizon is timelike.

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