{2+2} Formalism in General Relativity

Abstract

The importance in General Relativity of different types of initial value problems (i.v.p’s), especially those based on null or characteristic hypersurfaces, is discussed. This leads to the idea of decomposing space-time into two families of space-like hypersurfaces. Such a decomposition suggests that the freely specifiable initial data or gravitational degrees of freedom of the theory may be cast into the so-called conformal 2-structure. The formalism for describing this decomposition, called the co-variant orthogonal {2+2{ formalism, is outlined in some detail. Subsequently the refinement which enables particular holonomic and anholonomic i.v.p’s to be handled is introduced and illustrated by a particular i.v.p. (the anholonomic double null i.v.p.). A short discussion of computer implementation of formalisms is followed by some general remarks about the field of Numerical Relativity.