# What metric do you use to model a Galaxy

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I'm not an expert in GR, I'd like to if there is a standard practice in using a particular metric to model an isolated rotating Galaxy. I thought about Kerr-Newmann metric but I guess is not the standard practice. I guess is common practice to use Newton + a correction term, but in that case I'd like to know what term is it and where is comes from. Can someone help me with some references?

Thank you

It wouldn't make sence to model a galaxy with GR, that would use a lot of computer ressources and you wouldn't notice the difference to Newton since the field is weak and the velocities are slow compared to the speed of light. I would use the Newtonian field of a disk with variable density and a bulge, see http://notizblock.yukterez.net/viewtopic.php?t=120 for the equations.

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This depends on what do you need it for. You have to answer question such as

1. Do you want to describe motion at non-relativistic velocities near the galaxy?
2. Does the motion occur inside the galaxy or outside?
3. What do you assume about the morphology of the galaxy? (What type of Galaxy is it?)

If the answer to 1. is yes, you can typically use the metric in the Newtonian limit, i.e.

$$ds^2 = -(1 + 2 \Phi) dt^2 + (1 - 2 \Phi)(dx^2 + dy^2 + dz^2)$$

where $\Phi$ is the Newtonian potential sourced by the galactic matter. Now you "just" need to find the right $\Phi$. The answer depends a lot on questions 2. and 3. For instance, an almost spherically symmetric galaxy can be modeled by a spherically symmetric potential that is given simply by $\Phi = -GM(r)/r$, where $M(r)$ is the mass enclosed in the radius $r$. On the other hand, the outside potential of a flattened, almost axially symmetric galaxy can be modeled by potentials such as the Vinti potential or generally a multipolar expansion.

answered Mar 17, 2019 by (1,645 points)

Thank you Void. I think I got the idea and I would upvote your answer if I could... Unfortunately it seems I'm not yet able to vote :(

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