From In Wheeler and Taylor's 'Exploring Black Holes', on pages 3-12, the equation for energy in Schwarzschild geometry for an object in free fall is-(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{E}{m}=\left(1-\frac{2M}{r}\right)\frac{dt}{d\tau}=1[/tex]

where [itex]\tau[/itex] is proper time conventionally expressed in Schwarzschild geometry as [itex]d\tau=dt\sqrt{(1-2M/r)}[/itex]. This would appear to give an answer greater than 1.

I'm guessing that the Lorentz factor come into play as the object is in free-fall so that [itex]d\tau[/itex] is the sum of gravitational and velocity time dilation-

[tex]d\tau=dt\sqrt{1-\frac{2M}{r}} \cdot \sqrt{1-\frac{v^2}{c^2}}[/tex]

where [itex]v=\sqrt{(2M/r)}\ c[/itex] for an object in freefall. This would maintain e/m=1. Would this be correct?

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# Energy in Schwarzschild geometry

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