2

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
  • 16,329
Jayant
  • 21
  • Perfect time to bring up GR for engineers : https://www.springer.com/gp/book/9783642357978 – Slereah Apr 25 '18 at 08:57
  • Recommended reading: https://physics.stackexchange.com/q/363/25301 – Kyle Kanos Apr 25 '18 at 10:17
  • Welcome to PSE (physics stackexchange). I upvoted your question since you described your profile a bit. I suggest you fill your profile with some information about your strong points or interests. This helps people giving you a better answer. Click on any username here to see their profile for inspiration. I also suggest you give yourself a better username (user94458 is not very memorable). Look for recommended book on GR here or in meta or online. My suggestion here and always: MTW even if it is 45 years old. Carrol is also good and recent. cont.... – magma Apr 26 '18 at 07:46
  • cont...The book suggested by @KyleKanos might be cute, but it is like eating pizza in a Turkish pizzeria or eating baclava (Turkish delight) in an Italian pastry shop. Ultimately you want the real thing in the original setting. :-) – magma Apr 26 '18 at 07:49

1 Answers1

1

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
  • 147