An Introduction to Modern Astrophysics · Problem 17.17

Close Binary Star Systems — Carroll & Ostlie

Physics — Astrophysics · black-holes-angular-momentum

Problem

To obtain a crude estimate for the maximum angular momentum of a rotating black hole, imagine (obviously incorrectly!) that the black hole's mass is distributed uniformly throughout a solid sphere of radius RSR_S (the Schwarzschild radius). From basic physics, the moment of inertia of a uniform, rotating sphere is I=25MR2I = \frac{2}{5}MR^2, and the angular momentum of the sphere is L=IωL = I\omega, where ω\omega is the sphere's angular velocity. From this classical approach, estimate the maximum angular momentum of the solid sphere, and compare your answer with Eq. (17.29). (Be sure to specify any additional assumptions you have made.) What is the percentage error in your estimate compared to the exact result?

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