On 10/24/2014 11:43 AM, Warren D Smith wrote:
WDS: As far as I know, an important still-open problem is to find a way to glue the Kerr vacuum metric as the exterior, onto the metric of some realistic hunk of rotating matter as the interior, to get combined metric representing a rotating mass and its gravity field. Seems quite embarrassing that nobody has been able to do that. How hard can it be?
(But there are many successful ways to do this in the non-rotating case.) 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 --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).
But then the problem is what stress-energy tensor is implied by this hunk - nothing realistic.
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.
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. Brent
(Although, I suppose you could argue a solution of your sort genuinely was valid for describing a mass made of superfluid liquid helium... but helium is only superfluid in a rather small pressure & temperature set.)
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