AI 中文总结
该研究在四维时空中探究F(R)引力的黑洞解，分能量动量张量为零与非零情况推导解，引入四类新F(R)黑洞，计算热力学量并分析热稳定性，还研究了光子球与黑洞阴影。
AI 中文摘要
我们在四维时空中研究F(R)引力框架下的黑洞解，分别处理能量动量张量为零和非零的情况。我们证明，在无能量动量张量时，独立方程的数量足以得到里奇平坦解，无需预先给定F(R)函数，同时也能得到可变里奇标量的解。此外，对于非零能量动量张量，我们推导出常里奇标量和变里奇标量的精确解，从而引入新的带电黑洞。利用该新方法，我们不仅能得到广义相对论及此前已知的F(R)引力解，还引入了四类新的F(R)黑洞。我们计算了它们的热力学量，确认黑洞热力学第一定律的有效性，并通过热力学和几何方法分析这些新黑洞的热稳定性，最后在F(R)引力框架下研究了光子球和黑洞阴影。
英文摘要
We investigate black hole solutions in F(R) gravity within a four-dimensional spacetime, separately treating the cases of vanishing and nonvanishing energy momentum tensors. We demonstrate that in the absence of an energy momentum tensor, the number of independent equations is sufficient to obtain the Ricci flat solutions without the need for a prescribed F(R) function. In the same case, also the solutions with variable Ricci scalar can obtained too. Furthermore, for a nonvanishing energy momentum tensor, we derive exact solutions for both constant and variable Ricci scalars, thereby introducing new charged black holes. Utilizing this new method, we not only recover the general relativistic and previously known F(R) gravity solutions but also introduce four new classes of F(R) black holes. We calculate their thermodynamic quantities and confirm the validity of the first law of black hole thermodynamics. The thermal stability of these new black holes is analyzed using both thermodynamic and geometrical approaches. Finally, the photon spheres and black hole shadows are studied within the F(R) gravity framework.
Comments19 pages, 1 figure
