arXiv 0905.22222009-05-13gr-qcastro-ph.COhep-phhep-th

多维重力的形状

The shape of multidimensional gravity

Maxim Eingorn, Alexander Zhuk

备注：: 4 pages of Revtex4, 2 eps figures

摘要：

在一个额外维的情况下，如果四维空间具有拓扑$\mathbb{R}^3\times T$，则将著名的牛顿势$ϕ(r_3)=-G_N m/r_3$推广为紧致而优美的公式$ϕ(r_3,ξ)=-(G_N m/r_3)\sinh(2πr_3/a)[\cosh(2πr_3/a)-\cos(2πξ/a)]^{-1}$.这里，$r_3$是三维径向矢量的大小，$ξ$是额外维度，$a$是圆环$T$的周期。该公式适用于变量$r_3 \in [0,+\infty)$和$ξ\in [0,a]$的全范围，并且具有已知的渐近行为：$r_3>>a$的$ϕ\sim 1/r_3$和$r_4=\sqrt{r_3^2+ξ^2}<<a$的$ϕ\sim 1/r_4^2$。将所得公式应用于无限薄壳、壳、球和两个球，以显示与牛顿表达式的偏差。通常，这些修正在实验中观察到非常小。然而，在空间拓扑$\mathbb{R}^3\times T^{d}$的情况下，实验数据可以为我们提供额外维度的最大数量的限制。

英文摘要：

In the case of one extra dimension, well known Newton's potential $ϕ(r_3)=-G_N m/r_3$ is generalized to compact and elegant formula $ϕ(r_3,ξ)=-(G_N m/r_3)\sinh(2πr_3/a)[\cosh(2πr_3/a)-\cos(2πξ/a)]^{-1}$ if four-dimensional space has topology $\mathbb{R}^3\times T$. Here, $r_3$ is magnitude of three-dimensional radius vector, $ξ$ is extra dimension and $a$ is a period of a torus $T$. This formula is valid for full range of variables $r_3 \in [0,+\infty)$ and $ξ\in [0,a]$ and has known asymptotic behavior: $ϕ\sim 1/r_3$ for $r_3>>a$ and $ϕ\sim 1/r_4^2$ for $r_4=\sqrt{r_3^2+ξ^2}<<a$. Obtained formula is applied to an infinitesimally thin shell, a shell, a sphere and two spheres to show deviations from the newtonian expressions. Usually, these corrections are very small to observe at experiments. Nevertheless, in the case of spatial topology $\mathbb{R}^3\times T^{d}$, experimental data can provide us with a limitation on maximal number of extra dimensions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文