Logarithmic matching between past infinity and future infinity: The massless scalar field

Understand

Matching conditions relating the fields at the future of past null infinity with the fields at the past of future null infinity play a central role in the analysis of asymptotic symmetries and conservation laws in asymptotically flat spacetimes.

• These matching conditions can be derived from initial data given on a Cauchy hypersurface by integrating forward and backward in time the field equations to leading order in an asymptotic expansion, all the way to future and past null infinities.
• The standard matching conditions considered in the literature are valid only in the case when the expansion near null infinity (which is generically polylogarithmic) has no dominant logarithmic term.
• This paper is the first in a series in which we derive the matching conditions for a massless scalar field with initial conditions leading to dominant logarithms at null infinity.