Supertranslations at timelike infinity

Abstract

Abstract We propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. We present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. We show that the Lee-Wald symplectic form Ω(g, δ 1g , δ 2g ) does not get contributions from future timelike infinity with our boundary conditions. As a result, the “future charges” can be computed on any two-dimensional surface surrounding the sources at timelike infinity. We present expressions for supertranslation and Lorentz charges.

Keywords

• Classical Theories of Gravity
• Space-Time Symmetries