Hyperbolic positive energy theorem with electromagnetic fields

Abstract

Abstract. We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.

Positive energy theorem for (4+1)-dimensional asymptotically anti-de Sitter spacetimes

“…Proof: The proof is similar to the corresponding Poincaré inequalities in [2,28]. As C ∞ 0 (S) is dense in H 1 (M, S), we can take φ ∈ C ∞ 0 (S).…”

“…For the nontrivial second fundamental forms, Chruściel, Maerten and Tod [8] proved it by assuming the existence of center of AdS mass' coordinate systems [21,8], and the authors and Xie finally proved it for general case [27]. An extension involving electromagnetic fields was proved by the first-named author and Xu [28].…”

Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

“…Finally, Wang, Xie and Zhang proved the positive energy theorem for general case [20]. Its extension involving electromagnetic fields was proved by Wang and Xu [21].…”

The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting

“…There is a vast literature devoted to spinor proofs of positive mass theorem in both settings, see e.g. [CJL04], [CM06], [CMT06], [Mae06], [WX15], [XZ08], [Zha99], [Zha04]. The initial data sets we are considering in this paper are "hyperboloidal", that is we assume K → g at infinity.…”