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I have this expression for the gravitational force between 2 masses when the gr term is added:

$$F = - \frac{GMm}{r^2} + \frac{4G^2mM(M+m)}{r^4c^2}$$

which I got from the internet since I haven't bee able to find a similar expression in any book. But i'm not sure if it's right or needs fixing.

Is the second term in the force correct?

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1 Answers1

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I only know a little bit of GR. But by checking dimensions, it should be wrong.

$$\left[\frac{GM}{r^2c^2}\right]=\left[\frac{GM^2}{r}\right]\left[\frac{1}{Mc^2}\right]\left[\frac{1}{r}\right]=\left[\frac{1}{r}\right]$$

which is not dimensionless.

velut luna
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