Formal Definitions
A manifold M is asymptotically simple if it admits a conformal compactification such that every null geodesic in M has a future and past endpoints on the boundary of .
Since the latter excludes black holes, one defines a weakly asymptotically simple manifold as a manifold M with an open set U⊂M isometric to a neighbourhood of the boundary of, where is the conformal compactification of some asymptotically simple manifold.
A manifold is asymptotically flat if it is weakly asymptotically simple and asymptotically empty in the sense that its Ricci tensor vanishes in a neighbourhood of the boundary of .
Read more about this topic: Asymptotically Flat Spacetime
Famous quotes containing the words formal and/or definitions:
“I will not let him stir
Till I have used the approvèd means I have,
With wholesome syrups, drugs, and holy prayers,
To make of him a formal man again.”
—William Shakespeare (1564–1616)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)