Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes

Haotian Liu; Junji Jia

doi:10.1140/epjc/s10052-020-08496-5

paper

Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes

arXiv:2006.11125 · doi:10.1140/epjc/s10052-020-08496-5

Abstract

Total travel time $t$ and time delay $Δ t$ 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 $r_{s}$ and lens-detector distances $r_{d}$ , signal velocity $v$ , and asymptotic expansion coefficients of the metric functions. The time delay $Δ t$ to the leading order(s) were shown to be determined by the spacetime mass $M$ , spin angular momentum $a$ and post-Newtonian parameter $γ$ , and kinematic variables $r_{s}, r_{d}, v$ and source angular position $β$ . When $β ≪ a M / r_{s, d}$ , $Δ t$ 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 $β ≲ 1.5 \times 1 0^{- 5}$ [ $^{''}$ ], then $Δ t$ will be able to reach the $O (1)$ second level, which is well within the time resolution of current GRB, gravitational wave and neutrino observatories. Therefore measuring $Δ t$ in GL of these signals will allow us to constrain the spin of the Sgr A*.

arXiv comment20 pages, 4 figures, to match the published version

Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes

Abstract

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