Quasi-Local Penrose Inequalities with Electric Charge. (16th August 2021)

• Record Type: Journal Article
• Authors: Chen, Po-Ning; McCormick, Stephen
• Is Part Of: International mathematics research notices. Volume 2022:Number 22(2022)
• Page Start: 17333
• Page End: 17362
• Publication Date: 2021-08-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab215
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with nonnegative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein–Maxwell equations where the lower bound on mass depends also on electric charge, a charged Riemannian Penrose inequality. Here, we establish some quasi-local charged Penrose inequalities for surfaces isometric to closed surfaces in a suitable Reissner–Nordström manifold, which serves as a reference manifold for the quasi-local mass. In the case where the reference manifold has zero mass and nonzero electric charge, the lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Penrose inequality.