ADM and Bondi four-momenta for the ultrarelativistic Schwarzschild black hole

TL;DR

This paper demonstrates that the ultrarelativistic limit of the Schwarzschild black hole can be assigned consistent Bondi and ADM four-momenta, with the Bondi momentum being lightlike and matching the ADM momentum until radiation escapes.

Contribution

It shows how to assign physically consistent Bondi and ADM four-momenta to an ultrarelativistic Schwarzschild black hole, clarifying their behavior during radiation escape.

Findings

Bondi momentum is lightlike in the ultrarelativistic limit

Bondi and ADM momenta agree until radiation escapes

Space becomes flat after radiation leaves

Abstract

We argue that it is possible to assign Bondi as well as ADM four-momentum to the ultrarelativistic limit of the Schwarzschild black hole in agreement to what is expected on physical grounds: The Bondi-momentum is lightlike and equal to the ADM-momentum up to the retarded time when particle and radiation escape to infinity and drops to zero thereafter, leaving flat space behind.