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jmz34
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Homework Statement
An isolated, thin, rigid, spherical shell has mass M and radius R. If the shell is set slowly spinning with angular momentum J, show that inertial frames within the shell rotate at angular velocity w with respect to an observer at rest at infinity, where:
w=2GJ/(c^2*R^3)
Homework Equations
The Attempt at a Solution
Firstly I found the line element for r>R by neglecting terms greater than first order in a in the Kerr line element. This gave me a simple expression:
ds^2= ds^2(Swarzchild) + (4GJ(sin(theta))^2)/(c^2*r)
What is confusing me is the line element inside the shell. I was told that the line element is of Minkowski form but I can't really see why. If the line element were to be of Minkowski form why would we get frame dragging inside the shell?
If I can understand this then I can see that the problem can be done by matching up the 2 line elements at the suface of the shell r=R.
Thanks in advance.