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From: mike@bambi.UUCP (Michael Caplinger)
Newsgroups: net.physics
Subject: Re: Shape of a spinning black hole
Message-ID: <90@bambi.UUCP>
Date: Sun, 1-Sep-85 19:33:17 EDT
Article-I.D.: bambi.90
Posted: Sun Sep  1 19:33:17 1985
Date-Received: Mon, 2-Sep-85 04:19:50 EDT
References: <521@sri-arpa.ARPA>
Reply-To: mike@bambi.UUCP (Michael Caplinger)
Organization: Bell Communications Research
Lines: 20
Summary: 


No, even rotating black holes have spherical event horizons.  The radius
of the horizon is r = M + sqrt(M^2 - Q^2 - a^2), where M is the mass,
Q is the charge, and a is the angular momentum per unit mass (S/M).

However, the "static limit" of a rotating black hole is non-spherical.
The static limit is the surface at or below which an object cannot stay
motionless with respect to distant objects (that is, in an inertial frame.)
It's at a radius the same as the event horizon's, but with a cos^2(theta)
term multiplying the a^2 term above.  I'm not sure if that's an "oblate
spheroid" or not.

By the way, the shape of the Earth is not the same as that of a perfectly
fluid object with the same mass and angular momentum - it's "pear-shaped"
by some tens of meters in various directions.

	- Mike

The above equations are from Misner, Thorne, and Wheeler's GRAVITATION,
page 878-879.