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I am trying to learn general theory of relativity, my only source of knowledge is internet and books. I am a mechanical engineer by profession and not a physicist, please bear with my question.

Slereah
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Jayant
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1 Answers1

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The equations describing the motion of bodies in free fall are the geodesic equations associated with the spacetime manifold you are considering. You can find them in any textbook, as they are a central object in the study of general relativity. See for example this Wikipedia page.

Since you are asking for the case in which the mass is negligible, notice that the value of the mass, in this case, is irrelevant. The only crucial question regarding the mass $m$ is: is $m=0$ or $m>0$? This determines whether you should look for lightlike geodesics or timelike geodesics. But any positive value of $m$ will lead to the same set of solutions.

Edit: I realize now that, when you specify that $m$ is negligible, you probably mean that the body has to be regarded as a test particle. In that case, in fact, one can ignore the effect of $m$ on the metric and consider the latter as a fixed background.

dodosoft
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