Relation To Other Theories
Since they constitute a very simple and natural class of Lorentzian manifolds, defined in terms of a null congruence, it is not very surprising that they are also important in other relativistic classical field theories of gravitation. In particular, pp-waves are exact solutions in the Brans-Dicke theory, various higher curvature theories and Kaluza-Klein theories, and certain gravitation theories of J. W. Moffat. Indeed, B. O. J. Tupper has shown that the common vacuum solutions in general relativity and in the Brans/Dicke theory are precisely the vacuum pp-waves (but the Brans/Dicke theory admits further wavelike solutions). Hans-Jürgen Schmidt has reformulated the theory of (four-dimensional) pp-waves in terms of a two-dimensional metric-dilaton theory of gravity.
Pp-waves also play an important role in the search for quantum gravity, because as Gary Gibbons has pointed out, all loop term quantum corrections vanish identically for any pp-wave spacetime. This means that studying tree-level quantizations of pp-wave spacetimes offers a glimpse into the yet unknown world of quantum gravity.
It is natural to generalize pp-waves to higher dimensions, where they enjoy similar properties to those we have discussed. C. M. Hull has shown that such higher dimensional pp-waves are essential building blocks for eleven-dimensional supergravity.
Read more about this topic: Pp-wave Spacetime
Famous quotes containing the words relation to, relation and/or theories:
“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (1909–1943)
“The foregoing generations beheld God and nature face to face; we, through their eyes. Why should not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us, and not the history of theirs?”
—Ralph Waldo Emerson (1803–1882)
“A work of art that contains theories is like an object on which the price tag has been left.”
—Marcel Proust (1871–1922)