标题： 四维尺度相关的施瓦茨希尔德-反德西特/戴西黑洞：阴影和弱偏转角及灰体边界的研究 显示英文标题

标题： 4D scale-dependent Schwarzschild-AdS/dS black holes: study of shadow and weak deflection angle and greybody bounding

摘要： 我们研究了尺度依赖引力中Schwarzschild-AdS/dS黑洞的阴影、偏转角和灰体边界。 我们使用EHT数据来限制参数$\epsilon$。 我们发现，在$1\sigma$级别的不确定性内，$\epsilon M_0$在Sgr. A*中处于$10^{-11} - 10^{-16}$量级，而在M87*中为$10^{-11} - 10^{-17}$。 使用这些参数，我们探讨了静态观察者所感知的阴影半径的行为。 利用Sgr. A*和M87*的已知参数，我们发现即使使用相同的尺度参数，靠近宇宙学视界时阴影投射行为也不同。 我们探讨了在弱场极限下，对于大质量粒子和零质量粒子的偏转角$\hat{\alpha}$，并使用非渐近平坦版本的高斯-博内定理研究了有限距离的影响。 我们发现，$\hat{\alpha}$强烈依赖于大质量粒子。 对$\epsilon$的影响进行测试，使用 Sgr。 A* 仅在低碰撞参数点上有效。 对于 M87*，只有在 AdS 类型中的缩放黑洞可以在高碰撞参数下进行测试，但代价是$\hat{\alpha}$的值非常低。 我们研究了理论中从黑洞发出的标量场的灰体因子的严格界限，并展示了传输概率的界限。 研究了尺度相关引力对灰体因子的影响，结果表明，在这种情况下灰体因子的界限小于施瓦茨希尔德黑洞的界限。 显示英文摘要

摘要： We investigate the shadow, deflection angle, and the greybody bounding of a Schwarzschild-AdS/dS black hole in scale-dependent gravity. We used the EHT data to constrain the parameter $\epsilon$. We have found that within the $1\sigma$ level of uncertainty, $\epsilon M_0$ ranges at $10^{-11} - 10^{-16}$ orders of magnitude for Sgr. A*, and $10^{-11} - 10^{-17}$ for M87*. Using these parameters, we explored how the shadow radius behaves as perceived by a static observer. Using the known parameters for Sgr. A* and M87*, we found different shadow cast behavior near the cosmological horizon even if the same scaling parameters were used. We explored the deflection angle $\hat{\alpha}$ in the weak field limit for both massive and null particles, in addition to the effect of finite distances using the non-asymptotically flat version of the Gauss-Bonnet theorem. We have found that the $\hat{\alpha}$ strongly depends on massive particles. Tests on $\epsilon$'s effect using Sgr. A* is only along points of low impact parameters. For M87*, only the scaled BH in AdS type can be tested at high impact parameters at the expense of very low value for $\hat{\alpha}$. We study the rigorous bound on the greybody factor for scalar field emitted from black holes in the theory and show the bound on the transmission probability. The effects of the scale-dependent gravity on the greybody factors are investigated, and the results indicate that the bound on the greybody factor in this case is less than the bound for the Schwarzschild black hole.