- #1
Anamitra
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We are considering a stationary curved spacetime fabric.
Temporal separation[Physical]is given by:
[tex]{T}_{2}{-}{T}_{1}{=}{\int \sqrt {g}_{00}{dt}[/tex]
[Limits of integration extending from t1 to t2which are of course the coordinate times]
The above integral is path dependent,in the general case[depending on the nature of g(00)].So the physical separation of time in general is not unique for a pair of events.
To reconcile the matter ,g(00) should not depend on more than one coordinate[leaving aside t]or else[rather in a generalized way] the above integral should be independent of path.
Temporal separation[Physical]is given by:
[tex]{T}_{2}{-}{T}_{1}{=}{\int \sqrt {g}_{00}{dt}[/tex]
[Limits of integration extending from t1 to t2which are of course the coordinate times]
The above integral is path dependent,in the general case[depending on the nature of g(00)].So the physical separation of time in general is not unique for a pair of events.
To reconcile the matter ,g(00) should not depend on more than one coordinate[leaving aside t]or else[rather in a generalized way] the above integral should be independent of path.
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