Asymptotically Flat Spacetime - Applications

Applications

The notion of asymptotic flatness is extremely useful as a technical condition in the study of exact solutions in general relativity and allied theories. There are several reasons for this:

• Models of physical phenomena in general relativity (and allied physical theories) generally arise as the solution of appropriate systems of differential equations, and assuming asymptotic flatness provides boundary conditions which assist in setting up and even in solving the resulting boundary value problem.
• In metric theories of gravitation such as general relativity, it is usually not possible to give general definitions of important physical concepts such as mass and angular momentum; however, assuming asympotical flatness allows one to employ convenient definitions which do make sense for asymptotically flat solutions.
• While this is less obvious, it turns out that invoking asympotic flatness allows physicists to import sophisticated mathematical concepts from algebraic geometry and differential topology in order to define and study important features such as event horizons which may or may not be present.