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arXiv 2001.01460gr-qcastro-ph.COhep-phhep-th
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球紧化Kaluza-Klein模型中$f(R)$引力和理想流体的非线性效应

Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification

Ezgi Canay, Maxim Eingorn, Alexander Zhuk

备注：
v2 (matching the publication in European Physical Journal C) = v1 + minor changes + new Refs.; 14 pages, no figures
发表信息：
Eur. Phys. J. C 80, 379 (2020)
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摘要：

我们研究了与$f(R)$重力和背景完美流体的非线性相关的影响，表现在卡鲁扎-克莱因模型与球形紧化。背景时空受到大质量引力源的扰动，该引力源在外部空间是无压的，但在内部空间具有任意的状态方程（EoS）参数。作为非线性理想流体的特征，声速的平方在外部和内部空间中不等于背景EoS参数。在这种情况下，我们找到精确解的线性化爱因斯坦方程的扰动度量系数。对于非线性模型与$f^{\prime\prime}(R_0)\neq0$，我们表明，这些系数获得校正项的形式，两个求和汤川电位和在退化的情况下，解决方案减少到一个单一的汤川电位与一些“损坏”的前因子（在前面的指数函数），其中，除了标准的$1/r$长期，包含独立的三维距离$r$的贡献。在线性$f''(R)=0$模型中，我们将前人的研究推广到任意非线性理想流体的情形。我们还研究了外部空间中声速为零的非线性背景理想流体的特殊情况，并证明了只有在$f''(R_0)=0$的情况下才存在非平凡解。

英文摘要：

We study the effects associated with nonlinearity of $f(R)$ gravity and of the background perfect fluid manifested in the Kaluza-Klein model with spherical compactification. The background space-time is perturbed by a massive gravitating source which is pressureless in the external space but has an arbitrary equation of state (EoS) parameter in the internal space. As characteristics of a nonlinear perfect fluid, the squared speeds of sound are not equal to the background EoS parameters in the external and internal spaces. In this setting, we find exact solutions to the linearized Einstein equations for the perturbed metric coefficients. For nonlinear models with $f^{\prime\prime}(R_0)\neq0$, we show that these coefficients acquire correction terms in the form of two summed Yukawa potentials and that in the degenerated case, the solutions are reduced to a single Yukawa potential with some "corrupted" prefactor (in front of the exponential function), which, in addition to the standard $1/r$ term, contains a contribution independent of the three-dimensional distance $r$. In the linear $f''(R)=0$ model, we generalize the previous studies to the case of an arbitrary nonlinear perfect fluid. We also investigate the particular case of the nonlinear background perfect fluid with zero speed of sound in the external space and demonstrate that a non-trivial solution exists only in the case of $f''(R_0)=0$.

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