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:
“Whoever has a keen eye for profits, is blind in relation to his craft.”
—Sophocles (497–406/5 B.C.)
“Light is meaningful only in relation to darkness, and truth presupposes error. It is these mingled opposites which people our life, which make it pungent, intoxicating. We only exist in terms of this conflict, in the zone where black and white clash.”
—Louis Aragon (1897–1982)
“Generalisation is necessary to the advancement of knowledge; but particularly is indispensable to the creations of the imagination. In proportion as men know more and think more they look less at individuals and more at classes. They therefore make better theories and worse poems.”
—Thomas Babington Macaulay (1800–1859)