I am interested to know what Newton's second law (F=ma) looks like in general relativity. Looking at the geodesic equation, it appears to have some similarity. Multiply the mass of a particle by both sides and it looks like this:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]m\frac{d^2x^{\mu}}{ds^2}+m\Gamma^{\mu}_{\nu\lambda}\frac{dx^{\nu}}{ds}\frac{dx^{\lambda}}{ds} = 0[/tex]

The left side resembles 'ma' in F=ma. The above describes a particle influenced only by gravity, so now I wonder how the equation changes when other forces are present, electromagnetism for example. From web searching and looking in textbooks I do not find any modified version of the geodesic equation that would fit, but there are some that look similar. This is my best guess, where q is the particle's charge and A is a potential due to some field:

[tex]m\frac{d^2x^{\mu}}{ds^2}+m\Gamma^{\mu}_{\nu\lambda}\frac{dx^{\nu}}{ds}\frac{dx^{\lambda}}{ds} = q\frac{dx^{\nu}}{ds}\frac{dA^{\mu}}{dx^{\nu}}[/tex]

Is this equation correct? It seems the right hand side is the GR analog to 'F' in F=ma. If anyone can refer me to a textbook or publication with this kind of equation, I would appreciate it very much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# GR analog to F=ma

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**