Charge and antipodal matching across spatial infinity
Federico Capone, Kévin Nguyen, Enrico Parisini
Abstract
We derive the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end we provide a precise map between Bondi data at null infinity \mathscr{I} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>ℐ</mml:mi> </mml:mstyle> </mml:math> and Beig—Schmidt data at spatial infinity i^0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> in a context appropriate to the gravitational scattering problem and celestial holography. In addition, we explicitly match the various proposals of BMS charges at \mathscr{I} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>ℐ</mml:mi> </mml:mstyle> </mml:math> found in the literature with the conserved charges at i^0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> .