Lorentzian manifolds

Asymptotically flat spacetime

An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime. While this notion makes sense for any Lorentzian manifold, it is most often applied to a spacetime standing as a solution to the field equations of some metric theory of gravitation, particularly general relativity. In this case, we can say that an asymptotically flat spacetime is one in which the gravitational field, as well as any matter or other fields which may be present, become negligible in magnitude at large distances from some region. In particular, in an asymptotically flat vacuum solution, the gravitational field (curvature) becomes negligible at large distances from the source of the field (typically some isolated massive object such as a star). (Wikipedia).

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Weyl metrics | De Sitter universe | Einstein field equations | Exact solutions in general relativity | Schwarzschild metric | Vacuum solution (general relativity) | Taub–NUT space | Fluid solution | Multipole expansion | Algebraic geometry | Boundary value problem | Kerr metric | Isolated system | Differential topology