2025/04/14 by Allen, Brian, Bryden, Edward, Kazaras, Demetre +1
#53C21 #83C57 #83C75 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2504.10641
We establish mass lower bounds of Penrose-type in the setting of 3-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal. More precisely, the lower bound consists of a universal constant multiplied by the square root of the minimal area required to enclose the outermost apparent horizon. Here the outermost apparent horizon may contain both marginally outer trapped (MOTS) and marginally inner trapped (MITS) components. The proof is based on the harmonic level set approach to the positive mass theorem, combined with the Jang equation and techniques arising from the stability argument of Dong-Song \citeDong-Song. As a corollary, we also obtain a version of the Penrose inequality for 3-dimensional asymptotically hyperbolic Riemannian manifolds.