Attractive gravity probe surfaces in higher dimensions

Abstract A generalization of the Riemannian Penrose inequality in n-dimensional space (3 ≤ n < 8) is done. We introduce a parameter α ($-\frac{1}{n-1}<\alpha \infty$) indicating strength gravitational field, and define refined attractive gravity probe surface (refined AGPS) with α. Then, we show area for AGPS, $A \le \omega _{n-1} \left[ (n+2(n-1)\alpha )Gm /(1+(n-1)\alpha ) \right]^{\frac{n-1}{n-2}}$, where ωn − 1 standard unit (n 1)-sphere, G Newton’s constant m Arnowitt-Deser-Misner mass. The obtained applicable not only to surfaces strong regions such as minimal (corresponding limit → ∞), but also those weak existing near infinity $\alpha \rightarrow -\frac{1}{n-1}$) .