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This may seem like a silly question. However, what are the conditions for a matter source to produce a non-spherically symmetric gravitational field?

More specifically, can a spherical source produce a non-spherically symmetric field or is this nonsense?

UPDATE:

After some reading around. It appears that due to uniqueness theorems or "no hair" theorem for black holes, after sufficiently long times we tend to the conclusion that black holes can only be distinguished by 3 parameters: Mass (energy), charge and angular momentum. So shape of the body (pre-collapse) is essentially irrelevant. Have I understood this correctly?

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  • $\begingroup$ if mass distribution in that spherical source is inhomogeneous, why not? $\endgroup$
    – Kosm
    Commented Jun 11, 2017 at 11:28
  • $\begingroup$ @Kosm do you know of any papers or reference that perform such a task? $\endgroup$
    – Rumplestillskin
    Commented Jun 11, 2017 at 12:15
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    $\begingroup$ you can look for gravitational field of non-spherical bodies. For example you can imagine a ball with a high-density cube embedded in it. And densities outside of the cube (but still inside of the ball) being very small. Then you can approximate the gravitational field of such ball by that of a cube. $\endgroup$
    – Kosm
    Commented Jun 11, 2017 at 12:23
  • $\begingroup$ That is interesting. Have you seen this done somewhere? Would be interested to see the outcome $\endgroup$
    – Rumplestillskin
    Commented Jun 11, 2017 at 13:54
  • $\begingroup$ For gravitational field of a cube see arxiv.org/abs/1206.3857. There might be some works on grav. fields of disks, rods, certainly ellipses. $\endgroup$
    – Kosm
    Commented Jun 11, 2017 at 14:01

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I am responding to the edit:

yes, after the gravitational collapse, all of the information about the shape of the collapsing body will be sent away in gravitational radiation, and you will be left with a body described by those three parameters, up to the assumptions of the no-hair theorem.

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  • $\begingroup$ Do you have any reference where something like this is presented? I think this is fascinating. $\endgroup$
    – Rumplestillskin
    Commented Jun 14, 2017 at 0:45
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    $\begingroup$ @Rumplestillskin: how technical are you? This quickly gets into a lot of technical math. For the quick and easy version, the relativists' toolkit works through showing that under the assumption of spherical symmetry, the nordstrom metric is the unique vacuum solution. $\endgroup$
    – Zo the Relativist
    Commented Jun 14, 2017 at 0:50
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    $\begingroup$ In the words of my professor: you can't have a black hole in the shape of a chair. $\endgroup$
    – user12029
    Commented Jun 14, 2017 at 1:08

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