论文标题
球形对称和静态解决方案$ f（r）$重力与EM田地
Spherically symmetric and static solutions in $f(R)$ gravity coupled with EM fields
论文作者
论文摘要
$ f（r）$重力中的场方程解决方案是针对球形对称和静态空间的重力的。发现此配置中支持的模型必须具有参数形式$ f'（r）| _ {r} = m+n r $，带有$ m，n $常数，其价值和符号对解决方案以及$ f（r）$的形式和范围都有很大的影响。当$ n = 0 $时，$ f（r）= m r+m_0 $，并且找到了爱因斯坦 - bi解决方案。 When $m\neq 0$ and $n\neq0$, $f(R)$ is asymptotically equivalent to GR and the Schwarzschild and $f(R)$-Reissner-Nordström 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} $，显式$ f（r）= m r+2n \ sqrt {r}+m_0 $。最后，找到了$ f（r）$的非线性（$ m = 0 $）y的解决方案，标量曲率和参数函数$ f（r）$，并且绘制了某些特定值$ m $和$ n $的模型。
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-Nordström 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.
