论文标题
较高维度的吸引人的重力探针表面
Attractive gravity probe surfaces in higher dimensions
论文作者
论文摘要
在$ n $二维空间（$ 3 \ le n <8 $）中，Riemannian Penrose不平等的概括已完成。我们引入了一个参数$α$（$ - \ frac {1} {n-1} <α<\ infty $），指示重力场的强度，并用$α$定义了精致的有吸引力的重力探针表面（精制的AGP）。然后，我们显示了精制AGP的区域不等式，$ a \ leω_{n-1} \ left [（n+2（n-1）α）gm /（1+（n-1）α）\ right]^{\ frac {n-1} {n-1} {n-1} {n-2}}} $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ at $ ans $ ats $ empation Agps，$之间$（N-1）$ - 球体，$ G $是牛顿的重力常数，$ m $是Arnowitt-Deser-Misner Mass。获得的不平等不仅适用于强力区域中的表面，例如最小的表面（对应于$α\ to \ infty $），还适用于存在较弱的重力的那些（对应于lim lim lim lim $α\ to -\ frac {1}} {1} {n -1} $）。
A generalization of the Riemannian Penrose inequality in $n$-dimensional space ($3\le n<8$) is done. We introduce a parameter $α$ ($-\frac{1}{n-1}<α< \infty$) indicating the strength of the gravitational field, and define a refined attractive gravity probe surface (refined AGPS) with $α$. Then, we show the area inequality for a refined AGPS, $A \le ω_{n-1} \left[ (n+2(n-1)α)Gm /(1+(n-1)α) \right]^{\frac{n-1}{n-2}}$, where $A$ is the area of the refined AGPS, $ω_{n-1}$ is the area of the standard unit $(n-1)$-sphere, $G$ is Newton's gravitational constant and $m$ is the Arnowitt-Deser-Misner mass. The obtained inequality is applicable not only to surfaces in strong gravity regions such as a minimal surface (corresponding to the limit $α\to \infty$), but also to those in weak gravity existing near infinity (corresponding to the limit $α\to -\frac{1}{n-1}$).
