This work investigates the influence of the Lorentz symmetry breaking in the bending angle of massive particles and light for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances, and it is applicable to non-asymptotically flat spacetimes when considering the receiver viewpoint. In order to analyze the deflection of massive particles, we systematize the Ishihara method for its application in the Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant.

这项工作研究了洛伦兹对称性破缺对大黄蜂黑洞解的大质量粒子和光的弯曲角的影响。由于大黄蜂场的非零真空期望值，所分析的解决方案破坏了洛伦兹对称性。我们使用 Ishihara 方法，该方法允许我们研究有限距离内光的弯曲角，并且在考虑接收器视点时适用于非渐近平坦时空。为了分析大质量粒子的偏转，我们系统化了 Ishihara 方法在雅可比度量中的应用。这种系统化允许使用 Gauss-Bonnet 定理研究大质量粒子的偏转角。我们考虑两个背景：第一个是由 Bertolami 等人发现的。并且是渐近平坦的。第二个是最近由 Maluf 等人发现的。并且由于有效的宇宙常数而不是渐近平坦的。