Eur. Phys. J. Plus (2022) 137: 634
https://doi.org/10.1140/epjp/s13360-022-02846-w

Regular Article

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

¹ Inha University in Tashkent, Ziyolilar 9, 100170, Tashkent, Uzbekistan
² Akfa University, Milliy Bog’ Street 264, 111221, Tashkent, Uzbekistan
³ National University of Uzbekistan, 100174, Tashkent, Uzbekistan
⁴ Department of Physics, Zhejiang Normal University, 321004, Jinhua, China
⁵ Ulugh Beg Astronomical Institute, Astronomy Street 33, 100052, Tashkent, Uzbekistan
⁶ Shanghai Astronomical Observatory, 80 Nandan Road, 200030, Shanghai, China
⁷ Institute of Nuclear Physics, Ulugbek Street, 100214, Tashkent, Uzbekistan
⁸ Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kori Niyoziy 39, 100000, Tashkent, Uzbekistan

^a atamurotov@yahoo.com

Received: 15 April 2022
Accepted: 16 May 2022
Published online: 28 May 2022

Abstract

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 , the orbits approach the central compact object, while the effect of the Æther parameter 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.