On 10/31/2014 3:22 PM, Warren D Smith wrote:
Brent Meeker: It's probably pretty hard because you can't just have a rigid rotating hunk of matter (no rigid bodies in relativity). So you'd probably choose a perfect fluid (no viscosity) to model the matter with an appropriate equation of state to model the compressibility. No doubt it can be done numerically. Brent Meeker WDS: Just because rigid bodies do not exist, does not stop there from being a rigidly rotating hunk of matter (all interpoint-distances preserved as measured by the metric). BM: But then the problem is what stress-energy tensor is implied by this hunk - nothing realistic. --it could well be realistic. Consider a rigidly rotating baseball. Or asteroid Ceres. Nothing unrealistic about it.
Nothing unrealistic about rigid rotation. What would be unrealistic would be assuming the body is rigid, i.e. not taking account of change in the stress-energy tensor due to internal stresses of rotation. That's what make's it complicated.
WDS: Further, if you produced a solution with inviscid fluid and not preserving interpoint distances, then I would dispute your solution because viscosity presumably would cause some kind of energy loss. BM: Loss to where? The energy can't get out. The effect of viscosity would just be to make the stress-energy tensor more complicated and possibly even turbulent. ----the energy can and will get out. Viscous losses ==> heat ==> radiated photons ==> out.
True. But the rate of energy loss will be so slow it can be ignored to a very good approximation.
Almost all real fluids have viscosity, so therefore an inviscid fluid solution would not be realistic as a steady-state solution. A genuinely steady-state solution should exist with a Kerr exterior and realistic interior.
One possible class of "realistic interiors" -- perhaps even the only class -- would be "a rigidly rotating mass distribution." Prove or disprove: there exists an interior in this class, and a way to glue it onto a Kerr metric exterior. If does exist, then start finding examples. If it doesn't exist, that sounds like a great theorem.
I agree. For example a crystalline sphere that is rotating rigidly must have a Kerr metric exterior; although the sphere will suffer some distortion.
You've now almost gotten me to talk myself into trying to do exactly this...
Go for it. Brent