Relation To Other Exact Solutions
The Kerr vacuum is a particular example of a stationary axially symmetric vacuum solution to the Einstein field equation. The family of all stationary axially symmetric vacuum solutions to the Einstein field equation are the Ernst vacuums.
The Kerr solution is also related to various non-vacuum solutions which model black holes. For example, the Kerr–Newman electrovacuum models a (rotating) black hole endowed with an electric charge, while the Kerr–Vaidya null dust models a (rotating) hole with infalling electromagnetic radiation.
The special case of the Kerr metric yields the Schwarzschild metric, which models a nonrotating black hole which is static and spherically symmetric, in the Schwarzschild coordinates. (In this case, every Geroch moment but the mass vanishes.)
The interior of the Kerr vacuum, or rather a portion of it, is locally isometric to the Chandrasekhar–Ferrari CPW vacuum, an example of a colliding plane wave model. This is particularly interesting, because the global structure of this CPW solution is quite different from that of the Kerr vacuum, and in principle, an experimenter could hope to study the geometry of (the outer portion of) the Kerr interior by arranging the collision of two suitable gravitational plane waves.
Read more about this topic: Kerr Metric
Famous quotes containing the words relation to, relation, exact and/or solutions:
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“Unaware of the absurdity of it, we introduce our own petty household rules into the economy of the universe for which the life of generations, peoples, of entire planets, has no importance in relation to the general development.”
—Alexander Herzen (1812–1870)
“In the long-run every Government is the exact symbol of its People, with their wisdom and unwisdom; we have to say, Like People like Government.”
—Thomas Carlyle (1795–1881)
“Football strategy does not originate in a scrimmage: it is useless to expect solutions in a political compaign.”
—Walter Lippmann (1889–1974)