Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

TL;DR

This paper explores how the number of spatial dimensions affects the equilibrium and gravitational properties of perfect fluid stars, revealing that gravity is stronger in four dimensions and that a positive cosmological constant influences mass and density limits.

Contribution

It provides a general analysis of hydrostatic equilibrium for perfect fluid stars in arbitrary dimensions, highlighting the unique strength of gravity in four dimensions and the impact of a positive cosmological constant.

Findings

Gravity effects are strongest in 4D compared to higher dimensions.

A positive cosmological constant imposes lower bounds on mass and density.

The degree of compactification depends on the number of dimensions.

Abstract

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed.