Null infinity

In theoretical physics, null infinity is a region at the boundary of asymptotically flat spacetimes. In general relativity, straight paths in spacetime, called geodesics, may be space-like, time-like, or light-like (also called null). The distinction between these paths stems from whether the spacetime interval of the path is positive (corresponding to space-like), negative (corresponding to time-like), or zero (corresponding to null). Light-like paths physically correspond to physical phenomena which propagate through space at the speed of light, such as electromagnetic radiation and gravitational radiation. The boundary of a flat spacetime is known as conformal infinity, and can be thought of as the end points of all geodesics as they go off to infinity. The region of null infinity corresponds to the terminus of all null geodesics in a flat Minkowski space. The different regions of conformal infinity are most often visualized on a Penrose diagram, where they make up the boundary of the diagram. There are two distinct regions of null infinity, called past and future null infinity, which can be denoted using a script 'I' as ${\displaystyle {\mathcal {I}}^{+}}$ and ${\displaystyle {\mathcal {I}}^{-}}$. These two regions are often referred to as 'scri-plus' and 'scri-minus' respectively. Geometrically, each of these regions actually has the structure of a topologically cylindrical three dimensional region.

The study of null infinity originated from the need to describe the global properties of spacetime. While early methods in general relativity focused on the local structure built around local frames of reference, work beginning in the 1960s began analyzing global descriptions of general relativity, analyzing the structure of spacetime as a whole. The original study of null infinity originated with Roger Penrose's work analyzing black hole spacetimes. Null infinity is a useful mathematical tool for analyzing behavior in asymptotically flat spaces when limits of null paths need to be taken. For instance, black hole spacetimes are asymptotically flat, and null infinity can be used to characterize radiation in the limit that it travels outward away from the black hole. Null infinity can also be considered in the context of spacetimes which are not necessarily asymptotically flat, such as in the FLRW cosmology.