I just came across this expression(adsbygoogle = window.adsbygoogle || []).push({});

[tex]ds^2 = (1+gz/c^2)^2(cdt)^2 - dx^2 - dy^2 - dz^2[/tex]

in entry #19 of this thread https://www.physicsforums.com/showthread.php?t=227753[/URL] for the metric of a uniform gravitational field. Is this correct? I was wondering because it yields

[tex]\frac{d\tau}{dt}=(1+\frac{gz}{c^2}) [/tex]

for a stationary clock, but if

[tex]\frac{d\tau}{dt}=\sqrt{1-\frac{v_{esc}^2}{c^2}}

[/tex]

between any two points of different gravitational potential, then we should get

[tex]\frac{d\tau}{dt}=\sqrt{1-\frac{2gz}{c^2}}[/tex]

instead. Here z=0 is the ceiling of the elevator/spaceship and z>0 as we move towards the floor, but even if we switch that around (so that z=0 is the floor and z>0 as we move towards the ceiling) it doesn't explain what happened to the "2" or the radical sign.

Can someone point out the flaw(s) in my reasoning? Is the escape velocity/time dilation relationship not applicable here? Thanks.

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# Elevator metric

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