https://doi.org/10.1140/epjc/s10052-020-08496-5
Regular Article - Theoretical Physics
Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes
1
School of Physics and Technology, Wuhan University, 430072, Wuhan, China
2
MOE Key Laboratory of Artificial Micro- and Nano-structures, Center for Astrophysics, School of Physics and Technology, Wuhan University, 430072, Wuhan, China
Received:
19
June
2020
Accepted:
25
September
2020
Published online:
9
October
2020
Total travel time t and time delay 
between images of gravitational lensing (GL) in the equatorial plane of stationary axisymmetric (SAS) spacetimes for null and timelike signals with arbitrary velocity are studied. Using a perturbative method in the weak field limit, t in general SAS spacetimes is expressed as a quasi-series of the impact parameter b with coefficients involving the source-lens distance 
and lens-detector distances
, signal velocity v, and asymptotic expansion coefficients of the metric functions. The time delay to the leading order(s) were shown to be determined by the spacetime mass M, spin angular momentum a and post-Newtonian parameter 
, and kinematic variables 
and source angular position 
. When 
, is dominated by the contribution linear to spin a. Modeling the Sgr A* supermassive black hole as a Kerr–Newman black hole, we show that as long as 
[
], then will be able to reach the 
second level, which is well within the time resolution of current GRB, gravitational wave and neutrino observatories. Therefore measuring in GL of these signals will allow us to constrain the spin of the Sgr A*.
© The Author(s) 2020
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