From: Paul Fennessey

Grade: grad (science)

City: Prunedale, State/Prov.: CA Country: USA

Area: Astronomy

Message ID Number: 951193988.As

If angular momentum is conserved and a large (10+solar mass)collapses into a black hole will it's spin exceed the speed of light if its rotation is equal or greater than our suns?

Strictly speaking, it does not quite make sense to compare the "speed of
rotation" of a black hole (BH) with *c*,
the speed of light, because a BH, unlike a planet or a star,
has no physical surface that can have a velocity.
Even at the event horizon
(the one-way surface, from which neither light nor matter can escape, and which
shrouds the central singularity),
an observer -- if one could somehow manage to survive the tidal
stresses there -- would find nothing but empty space.
Of course, almost the most basic principle of Special Relativity is that no
velocity can be attached to space itself.

Yet a BH may have angular momentum, and thus may be considered to rotate in
somewhat the same sense that an elementary particle's spin is an intrinsic
rotation.
A rotating (uncharged) BH is described by the Kerr (1963) solution to
Einstein's equations for the gravitational field.
(Einstein's equations are a set of partial differential equations defining
the curvature of spacetime in terms of the distribution of mass and energy;
they play much the same role in the theory of gravitation as Maxwell's equations
play in electromagnetic theory.)
Such Kerr BHs are characterized by mass *M* and angular momentum *J*.
It turns out that, for a given *M*, there is a maximum allowed *J*:

So in this somewhat loose sense, there actually is a maximum "rotation speed" for a BH.

Whether a particular star has *J* over or under the limit depends on
its mass, rotation speed, and spatial extent.
Since real stars tend to have most of their mass concentrated near their
centers, the internal distribution of mass, rather than just the optical
diameter, is important.
The Sun, due to its rather slow (25-day) rotation, has an angular momentum
of about
1.63x10^{48}
gm-cm^{-2}-s^{-1}
(assuming uniform rotation throughout, and standard models
for the interior mass distribution; Allen 1970),
which is only 0.185 of the maximum
value allowed were it to somehow collapse to become a BH.
But a rapidly rotating massive star will typically have an angular momentum
exceeding its *J _{max}*,
and such stars must shed angular momentum and some mass
before they could form BHs.

Exactly how this might be accomplished remains incompletely understood in detail, despite substantial theoretical interest and investigation in recent years. Observationally, as techniques have improved, more and more candidate BHs have been seen to be associated with narrow jets or beams, in which matter is ejected at relativistic speeds. Such jets may well be related to the need for compact systems to shed angular momentum as matter is accreted by the central object.

Misner, Thorne, and Wheeler (1973) exhaustively discuss the General Relativity background needed to fill in all the details of this rather sketchy discussion, and also treat black holes particularly thoroughly.

REFERENCES:

Allen, C. W. 1970 "Astrophysical Quantities", Althione Press.

Kerr, R. P. 1963 Phys Rev Lett 11, 237.

Misner, Thorne, and Wheeler, 1973, "Gravitation", Freeman.

Shapiro and Teukolsky 1983, "Black Holes, White Dwarfs, and Neutron Stars" (New York: Wiley).