We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future asymptotically flat null cone, and show that the solution exists uniformly around the null cone for general such initial data. Therefore, the solution contains a piece of the future null infinity. The initial data are not required to be small and the decaying condition is consistent with those in the works of  and .
The authors are partially supported by NSFC 11521101. The first author is also partially supported by NSFC 11501582.
"On the local extension of the future null infinity." J. Differential Geom. 110 (1) 73 - 133, September 2018. https://doi.org/10.4310/jdg/1536285627