Testing the Einstein-Æther gravity: particle dynamics and gravitational lensing

The optical and energetic properties of the black hole (BH) in the Einstein-Æther gravity are investigated. In the first part of the paper, the motion of massive and massless particles including effective potential is studied under the influence of parameters of Einstein-Æther gravity. We have obtained the horizon structure, photon orbits and Innermost Stable Circular Orbit (ISCO) radius of mass particles around the BH in Einstein-Æther theory. It is shown that with the increase in the Æther parameter c₁₄, the orbits approach the central compact object, while the effect of the Æther parameter c₁₃ is opposite and moves the ISCO outwards. In the second part, gravitational weak lensing is studied in more detail using the general method and the deflection angle of light rays around the black hole in plasma environment is derived. The magnification of image brightness is obtained using the angle of deflection of the light rays. Finally, we explored energy extracted from BH in Einstein-Æther gravity using the BSW (Banados–Silk–West) effect we have got expression of centre mass energy.