标题： 强引力透镜和洛伦兹破坏理论下的带电黑洞霍金谱 显示英文标题

标题： Strong lensing and Hawking spectra of charged black hole under Lorentz violation theory

摘要： 在本文中，我们研究了在蜜蜂引力中的类似Reissner-Nordström黑洞（RN-like BH）周围的强引力透镜效应。我们计算了偏转角、光子球半径、角分离、相对论图像特征、爱因斯坦环和时间延迟等透镜量。通过将像Sgr A*、M87*、NGC 1332、NGC 4649等超大质量黑洞（SMBHs）作为类似RN的黑洞，我们计算了透镜观测量并与与Reissner-Nordström黑洞（RNBH）相关的观测量进行了比较。还计算了类似Reissner-Nordström-de Sitter黑洞（RNdS-like BH）的质量为零的狄拉克场扰动的准正则模式（QNMs）。我们讨论了QNMs频率的实部和虚部随着$Q$和$L$的变化行为。结果显示，随着$L$的增加，阻尼率和振荡频率会减少，但$Q$的增加则产生相反的效果。我们进一步探讨了LIGO和LISA检测QNMs的可行性，并研究了$L$和$Q$对可检测黑洞质量范围的影响。 此外，我们研究了bumblebee引力中类似RNdS黑洞的灰体因子（GF）的行为，并发现波传输的概率随着$L$的增加而增加，但随着$Q$的增加而减少。 对于不同值的$L$和$Q$，吸收截面和霍金辐射的稀疏性也进行了图形分析。 显示英文摘要

摘要： In this paper, we investigate the strong gravitational lensing effects around the Reissner-Nordstr{\"o}m-like black hole (RN-like BH) in bumblebee gravity. We calculate the lensing quantities such as deflection angle, radius of the photon sphere, angular separation, relativistic image characteristics, Einstein ring and time delay. By taking the supermassive black holes (SMBHs) like Sgr A*, M87*, NGC 1332, NGC 4649 etc. as RN-like BH, we compute the lensing observables and compare with the observables associated with the Reissner-Nordstr\"om black hole (RNBH). The quasinormal modes (QNMs) of massless Dirac field perturbation of Reissner-Nordstr{\"o}m-de Sitter-like (RNdS-like) BH are also calculated. We discuss the behaviour of both real and imaginary parts of QNM frequencies with varying of $Q$ and $L$. It shows the damping rate and the oscillation frequency decrease with increasing $L$ but it has the opposite effect for the increase of $Q$. We further explore the detectability of QNMs by LIGO and LISA, and study the impact of $L$ and $Q$ on the detectable BH mass range. Further, we investigate the behaviour of greybody factor (GF) of RNdS-like BH in bumblebee gravity and find that the probability of wave transmission increases with increasing $L$ but decreases with the increase of $Q$. The behaviour of absorption cross section and sparsity of Hawking radiation for different values of $L$ and $Q$ are also analysed graphically.