arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0907.5371hep-thastro-ph.HEgr-qchep-ph
收藏

非相对论极限下的多维引力

Multidimensional gravity in non-relativistic limit

Maxim Eingorn, Alexander Zhuk

备注：
RevTex4, 4 pages, 3 figures
发表信息：
Phys.Rev.D80:124037,2009
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

在拓扑为$M_{3+d}=\mathbb{R}^3\times T^d$的多维空间中，求出了Poisson方程的精确解.该解描述了从距离大于环面周期（额外维尺寸）的牛顿行为$1/r_3$到相反极限的多维行为$1/r^{1+d}_{3+d}$的平滑过渡。在一个额外维$d=1$的情况下，引力势用简洁的公式表示。结果表明，在卡文迪什型实验中，对引力常量的修正可以达到牛顿引力常量$G_N$的测量精度。它是提出的模型，其中的测试质量涂抹在一些（或所有）额外的维度。在10维有3个模糊额外维的时空中，对于1TeV的基本普朗克尺度$M_{Pl(10)}$，3个剩余额外维的尺寸可以放大到亚毫米级.在所有额外维度都被涂抹的模型中，引力势与牛顿引力势完全一致。然而，层次问题可以在这些模型中解决。

英文摘要：

It is found the exact solution of the Poisson equation for the multidimensional space with topology $M_{3+d}=\mathbb{R}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior $1/r^{1+d}_{3+d}$ in opposite limit. In the case of one extra dimension $d=1$, the gravitational potential is expressed via compact and elegant formula. It is shown that the corrections to the gravitational constant in the Cavendish-type experiment can be within the measurement accuracy of Newton's gravitational constant $G_N$. It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale $M_{Pl(10)}$. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one. Nevertheless, the hierarchy problem can be solved in these models.

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。

↑