Year: 2025
Type: article
Abstract: We establish a lower bound on the total mass of the time slices of $$(n+1)$$ ( n + 1 ) -dimensional asymptotically flat standard static spacetimes under the timelike convergence condition (TCC). The inequality can be viewed equivalently as a Minkowski-type inequality in these spaces, i.e. as a lower bound on the total mean curvature of the boundary, and thus extends inequalities from [4, 20, 23], and [11]. Equality is achieved only by slices of Schwarzschild space and is related to the characterization of quasi-spherical static vacuum metrics from [11]. As a notable special case, we obtain the Riemannian Penrose inequality in all dimensions for static spaces under the TCC.
Source: Journal of Geometric Analysis
Author: Brian Harvie
Institution: University of Copenhagen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: Københavns Universitet
OpenAlex ID: W4415443661