arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1202.4773gr-qcastro-ph.HEhep-phhep-th
收藏

Kaluza-Klein模型中引力质量张力的意义

Significance of tension for gravitating masses in Kaluza-Klein models

Maxim Eingorn, Alexander Zhuk

备注：
8 pages, no figures
发表信息：
Physics Letters B 716 (2012) 176-178
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文考虑内部空间具有球面紧化的六维Kaluza-Klein模型。在这里，我们调查的情况下，裸露的引力紧凑的对象与dustlike状态方程$\hat p_0=0$在外部（我们的）空间和任意状态方程$\hat p_1=Ω\hat\varepsilon$在内部空间，其中$\hat \varepsilon$是能量密度的源。这种引力质量在外部空间是球对称的，在内部空间均匀分布。在弱场近似下，内部空间体积的共形变化产生汤川势与通常的牛顿引力势的混合。对于足够大的汤川质量，这种混合是可以忽略的，外部时空的度规系数符合广义相对论的相应表达式。然后，这些模型满足经典引力检验。然而，我们表明，引力质量获得有效的相对论压力的外部空间。这种压力与对致密天体的观测相矛盾（例如，太阳）。等式$Ω=-1/2$（即张力）是在外部空间中保持尘埃状态方程的唯一可能性。因此，尽管与引力实验的$Ω$的任意值的协议，张力（$Ω=-1/2$）所考虑的模型起着至关重要的作用。

英文摘要：

In this letter, we consider the six-dimensional Kaluza-Klein models with spherical compactification of the internal space. Here, we investigate the case of bare gravitating compact objects with the dustlike equation of state $\hat p_0=0$ in the external (our) space and an arbitrary equation of state $\hat p_1=Ω\hat\varepsilon$ in the internal space, where $\hat \varepsilon$ is the energy density of the source. This gravitating mass is spherically symmetric in the external space and uniformly smeared over the internal space. In the weak field approximation, the conformal variations of the internal space volume generate the admixture of the Yukawa potential to the usual Newton's gravitational potential. For sufficiently large Yukawa masses, such admixture is negligible and the metric coefficients of the external spacetime coincide with the corresponding expressions of General Relativity. Then, these models satisfy the classical gravitational tests. However, we show that gravitating masses acquire effective relativistic pressure in the external space. Such pressure contradicts the observations of compact astrophysical objects (e.g., the Sun). The equality $Ω=-1/2$ (i.e. tension) is the only possibility to preserve the dustlike equation of state in the external space. Therefore, in spite of agreement with the gravitational experiments for an arbitrary value of $Ω$, tension ($Ω=-1/2$) plays a crucial role for the considered 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。

↑