Time delay of photons coupled to Weyl tensor in a regular phantom black hole
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Regular Article - Theoretical Physics
Time delay of photons coupled to Weyl tensor in a regular phantom black hole Xu Lu1,2 , Yi Xie1,2,a 1 2
School of Astronomy and Space Science, Nanjing University, Nanjing 210023, China Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education, Nanjing 210023, China
Received: 9 May 2020 / Accepted: 4 July 2020 / Published online: 15 July 2020 © The Author(s) 2020
Abstract Time delay of the photons coupled to the Weyl tensor in a regular phantom black hole is investigated in both weak and strong deflection gravitational lensing. We find that the time delay in the weak deflection lensing strongly depends on the phantom hair while the delay in the strong deflection lensing is significantly affected by the hair and the strength of the coupling. We suggest that it is necessary to measure these two kind of time signals for fully understanding and distinguishing such an interaction beyond the standard Einstein–Maxwell theory.
1 Introduction A new era of strong gravitational physics has come with the direct detections of gravitational waves from binary black holes [1–6] and with the direct imaging the shadow of the supermassive black hole M87* in the center of galaxy M87 [7–12]. Black holes are ideal laboratories for probing nature of gravity in the extreme environments and regimes for searching new phenomena beyond the standard models. Gravitational lensing is a straightforward and magnificent manifestation of the interaction between the gravitational and electromagnetic fields. It not only provides numerous insight into black holes but also plays a critical role in shaping their apparent looks [13]. The gravitational lensing with a weak deflection of light ray has become an indispensable instrument in astronomy [14–17] and gravitational physics [18–22]. The gravitational lensing with a strong deflection of light ray is the essential to raise the shadow [23] and relativistic images [24] of black holes, since the photons might surround a black hole for several loops [25,26]. It benefits understanding black holes [27–31] and telling difference of them [32–41]. a e-mail:
[email protected] (corresponding author)
Most studies on weak and strong deflection gravitational lensing assumed that the standard Einstein-Maxwell theory is valid [42,43], whereas new interactions beyond that could also exist. One-loop vacuum polarization on the quantum electrodynamics might make photons travel superluminally [44] due to the tidal gravitational forces caused by the quantum corrections, but this effect is extremely small because it depends on the square of the Compton wavelength of the electron. More general couplings between the gravitational and electromagnetic fields were also proposed [45,46] and were widely investigated in the context of astrophysics [47–50] and black hole physics [51–53]. The gravitational and electromagnetic fields might interact via the Weyl tensor, which was examined for holographic conductivity and superconductors [54–61] and for the e
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