The characteristic initial value problem in general relativity

2020.12.17（星期四），14:00-15:00

点：晨兴中心210教室

要：Applying Luk’s strategy, we revisit the local existence of characteristic initial value problem (CIVP) of Einstein field equation by using Newman-Penrose (NP) formalism under Stewart’s gauge. We provide some new insights of the structural properties of the NP equation as well as some technical details. With the same strategy, we analyze the asymptotic CIVP for the conformal Einstein field equations (CEFE) and demonstrate the local existence of solutions along a narrow rectangle along null infinity which, in turn, corresponds to an infinite domain in the asymptotic region of the physical spacetime. This result improves the work by Kannar on the local existence of solutions to the CIVP by means of Rendall’s reduction strategy. Based on the aforementioned work, we make use of a CIVP for the CEFE to provide an alternative proof of local extension of null infinity given by Li and Zhu.