I am well aware of one-dimensional stellar models:
The simplest commonly used model of stellar structure is the spherically symmetric quasi-static model, which assumes that a star is in a steady state and that it is spherically symmetric. It contains four basic first-order differential equations: two represent how matter and pressure vary with radius; two represent how temperature and luminosity vary with radius.
But what if we moved from spherical symmetry to cylindrical symmetry? Did somebody already set up all equations and solve them for general rotational symmetric ellipsoid?
What would be the (intutive) results of such a stellar model? I am sure, somebody solved the equations already and I am just missing the appropriate search terms.
- The mathematics of egg shape gives a brief mathematical background about one of my favorite mathematical objects
Cylindrical symmetry is not as hypothetical as it might sound:
- Ashley Strickland wrote for CNN about "Unusual tear-drop shaped, half-pulsating star discovered by amateur astronomers"
- WASP-12b is is reviewed by NASA as An egg-shaped planet.
The pre-print by E.C. & L.V. Nolan On isotropic cylindrically symmetric stellar models seems to cover the topic, but is not too intuitive.