; Peng, Yuxuan
; Xu, Jianfei] Univ Sci & Technol China, Interdisciplinary Ctr Theoret Study, Hefei 230026, Anhui, Peoples R China
; [Cao, Li-Ming] Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China
We consider a self-gravitating system containing a globally timelike Killing vector and a nonlinear Born-Infeld electromagnetic field and scalar fields. We prove that under certain boundary conditions (asymptotically flat/anti-de Sitter) there cannot be any nontrivial field configurations in the spacetime. To explore nontrivial solutions, one should break any of the conditions we imposed. The case with another type of nonlinear electromagnetic field is also analyzed, and similar conclusions have been obtained under certain conditions.