2026/07/31 by Tuan Dolmen
Mathematics · Physics and Astronomy · #math.DG #gr-qc
arxiv created 2026/07/31 · arxiv updated 2026/08/03
We prove the Penrose inequality with charge under the 2-convexity condition recently introduced by Dong. More precisely, given a complete, connected and asymptotically flat Einstein-Maxwell initial data set (M,g,k; E,B) satisfying the charged dominant energy and the 2-convexity conditions, with divergence-free electromagnetic vector fields (E,B) and a connected outermost past apparent horizon Σ that satisfies |Σ| ≥ 4πq2 - where q is the total charge - we show that the following inequality for the ADM mass m holds: m≥ √((|Σ|)/(16π)) + q2 √\fracπ|Σ|, with equality if and only if k ≡ 0 and (M,g;E,B) is isometric to a canonical slice of sub-extremal Reissner-Nordström spacetime. Building on Dong's proof of the uncharged case, we use his P-inverse mean curvature flow and its weak formulation, which only depends on (g,P) and hence applies to the charged setting unchanged. The novelty of our work is the modification of the monotonicity formula to account for the additional charge term. For time-symmetric data (k ≡ 0), the flow reduces to the classical inverse mean curvature flow and our monotonicity formula to Jang's monotonicity of the charged Hawking mass, recovering the charged Riemannian Penrose inequality.