标题： 偏转角、准正则模和$f(\mathcal{T}, \mathcal{B})$引力中德西特黑洞的光学性质 显示英文标题

标题： Deflection angle, quasinormal modes and optical properties of a de Sitter black hole in $f(\mathcal{T}, \mathcal{B})$ gravity

摘要： 当前研究旨在考察边界项对静态球对称黑洞在由$f(\mathcal{T}, \mathcal{B})$函数描述的修改引力中光线弯曲角的影响。 为了实现这一目标，我们采用 Ishihara\textit{等.}方法，该方法使我们能够在非渐近平坦时空中计算位于透镜物体有限距离处的接收器和光源的光线偏折角。 此方法考虑了接收器的视角，由于非渐近平坦时空， resulting 的偏折角会随着与透镜物体距离的增加而发散。 然而，这种发散可以通过边界项参数$c_0$进行调节。 对于参数$c_0$的较小值，在观测者和光源的有限范围内可以最小化发散。 此外，我们使用渐近迭代方法（AIM）和 Padé 平均六阶 WKB 近似方法计算黑洞背景下的无质量标量扰动的准正则模。 我们的研究结果表明，实数准正则模和阻尼率显著受到模型参数$c_0$的影响。 随后，我们研究了黑洞的两个光学特性，即阴影和发射率。 我们的结果表明，随着边界项参数$c_0$的增加，阴影的大小增加，蒸发率减少。 显示英文摘要

摘要： The current study aims to examine the impact of the boundary term on the bending angle of light for a static spherically symmetric black hole in the modified gravity described by the $f(\mathcal{T}, \mathcal{B})$ function. To accomplish this objective, we employ the Ishihara \textit{et al.}~method, which enables us to compute the deflection angle of light for a receiver and source situated at finite distances from a lens object in a non-asymptotically flat spacetime. This method considers the receiver's viewpoint, and the resulting deflection angle diverges as the distance from the lens object increases, owing to the non-asymptotically flat spacetime. Nevertheless, the divergence can be regulated by the boundary term parameter $c_0$. For lower values of the parameter $c_0$, the divergence can be minimized within the finite range of the observer and source. Furthermore, we calculate the quasinormal modes of massless scalar perturbations in the black hole's background using the asymptotic iteration method (AIM) and Pad\'e averaged sixth-order Wentzel-Kramers-Brillouin (WKB) approximation method. Our findings indicate that the real quasinormal modes and damping rates are significantly impacted by the model parameter $c_0$. Subsequently, we investigate two optical characteristics of the black hole, namely the shadow and the emission rate. Our results show that with an increase in the boundary term parameter $c_0$, the shadow's size increases, and the evaporation rate decreases.