One term I fully understand yet I have never seen how one actually does the calculation is the local gravity a particle feels in a gravitational field.(adsbygoogle = window.adsbygoogle || []).push({});

Now, I honestly feel this is as stupid of a question as they come, but intuitively I'd say, if I wanted a(r), the acceleration as a function of the radius (useful for things like Hawking temperature), you simply take your geodesic equation

[tex]{{d^2 x^{\mu}}\over{d\lambda^2}} + \Gamma^{\mu}_{\alpha \beta} {{dx^{\alpha}}\over{d\lambda}} {{dx^{\beta}}\over{d\lambda}} = 0[/tex]

to find the acceleration as a function of the radial distance, multiply by the redshift, and do your usual simple radially-infalling particle and wala, local acceleration.

And what is the physical interpretation? My assumption is that it's the acceleration felt in the test particle's frame. Correct? Naive? :)

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# Local gravity calculation

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