Lichnerowicz-Type Theorems for Self-gravitating Systems with Nonlinear Electromagnetic Fields
Li-Ming Cao, Yuxuan Peng, Jianfei Xu
TL;DR
This paper proves that under specific boundary conditions, self-gravitating systems with nonlinear electromagnetic and scalar fields cannot have nontrivial configurations, extending Lichnerowicz-type theorems to these complex fields.
Contribution
It establishes no-go theorems for nontrivial solutions in self-gravitating systems with nonlinear Born-Infeld electromagnetic fields and scalar fields under certain boundary conditions.
Findings
No nontrivial configurations under asymptotically flat/AdS conditions.
Similar no-go results for other nonlinear electromagnetic fields.
Conditions needed to potentially allow nontrivial solutions.
Abstract
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/AdS) there can't 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.
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