Open Problems
The Kerr vacuum is often used as a model of a black hole, but if we hold the solution to be valid only outside some compact region (subject to certain restrictions), in principle we should be able to use it as an exterior solution to model the gravitational field around a rotating massive object other than a black hole, such as a neutron star--- or the Earth. This works out very nicely for the non-rotating case, where we can match the Schwarzschild vacuum exterior to a Schwarzschild fluid interior, and indeed to more general static spherically symmetric perfect fluid solutions. However, the problem of finding a rotating perfect-fluid interior which can be matched to a Kerr exterior, or indeed to any asymptotically flat vacuum exterior solution, has proven very difficult. In particular, the Wahlquist fluid, which was once thought to be a candidate for matching to a Kerr exterior, is now known not to admit any such matching. At present it seems that only approximate solutions modeling slowly rotating fluid balls are known. (Slowly rotating fluid balls are the relativistic analog of oblate spheroidal balls with nonzero mass and angular momentum but vanishing higher multipole moments.) However, the exterior of the Neugebauer–Meinel disk, an exact dust solution which models a rotating thin disk, approaches in a limiting case the Kerr vacuum.
Read more about this topic: Kerr Metric
Famous quotes containing the words open and/or problems:
“To open a book brings profit.”
—Chinese proverb.
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)