# What are the conditions for non-spherically symmetric gravitational fields in GR?

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?

• if mass distribution in that spherical source is inhomogeneous, why not? – Kosm Jun 11 '17 at 11:28
• @Kosm do you know of any papers or reference that perform such a task? – Rumplestillskin Jun 11 '17 at 12:15
• 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. – Kosm Jun 11 '17 at 12:23
• That is interesting. Have you seen this done somewhere? Would be interested to see the outcome – Rumplestillskin Jun 11 '17 at 13:54
• 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. – Kosm Jun 11 '17 at 14:01