标题： 球对称和静态的$f(R)$引力与电磁场耦合的解 显示英文标题

标题： Spherically symmetric and static solutions in $f(R)$ gravity coupled with EM fields

摘要： 在$f(R)$引力中找到了球对称和静态时空在Born-Infeld（BI）非线性电动力学中的场方程解。 发现在此配置中支持的模型必须具有参数形式$f'(R)|_{r}=m+n r$，其中$m,n$为常数，其值和符号对解有重大影响，以及对$f(R)$的形式和范围也有影响。 当$n=0$，$f(R)=m R+m_0$时，找到Einstein-BI解。 当$m\neq 0$和$n\neq0$，$f(R)$与 GR 渐近等价，且施瓦茨希尔德和$f(R)$-Reissner-Nordström 解在某些极限下被写出，同样地，如果$n>0$和$r\gg1$，$f(R)$可以作为级数近似和特殊情况找到，当$R_S=-\frac{m^2}{3n}$，显式地$f(R)=m R+2n\sqrt{R}+m_0$. 最后，在非线性 ($m=0$) 范围内，找到了 $f(R)$的解、标量曲率和参数函数$f(r)$，并绘制了一些特定值的 $m$和 $n$的模型。 显示英文摘要

摘要： Solutions of field equations in $f(R)$ gravity are found for a spherically symmetric and static spacetime in the Born-Infeld (BI) non-linear electrodynamics. It is found that the models supported in this configuration must have the parametric form $f'(R)|_{r}=m+n r$, with $m,n$ constants, whose value and sign have a strong impact on the solutions, as well as in the form and range of $f(R)$. When $n=0$, $f(R)=m R+m_0$ and the Einstein-BI solution is found. When $m\neq 0$ and $n\neq0$, $f(R)$ is asymptotically equivalent to GR and the Schwarzschild and $f(R)$-Reissner-Nordstr\"om solutions are written in some limits, likewise if $n>0$ and $r\gg1$, $f(R)$ can be found as a series approximation and as a particular case, when $R_S=-\frac{m^2}{3n}$, explicitly $f(R)=m R+2n\sqrt{R}+m_0$. Finally, the solutions, scalar curvature and parametric function $f(r)$ in the non-linear ($m=0$) regime of $f(R)$ are found, and some models for specific values of $m$ and $n$ are plotted.