The minimum mass of a spherically symmetric object in $D$-dimensions, and its implications for the mass hierarchy problem

Understand

The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity.

• These results follow rigorously from the Buchdahl inequalities in four dimensional de Sitter space.
• In this work, we obtain the generalized Buchdahl inequalities in arbitrary space-time dimensions with $\Lambda \neq 0$ and consider both the de Sitter and anti-de Sitter cases.
• The dependence on $D$, the number of space-time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained.