论文标题
使用固定轴对称空间的时间延迟来限制时空旋转
Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes
论文作者
论文摘要
总的旅行时间$ t $ t $ t $ t $ t $Δt$在重力镜头图像（GL）之间的赤道平面（SAS）的赤道平面（SAS）空位的赤道平面，用于null和Timelike信号，并研究了任意速度。使用弱场限制中的扰动方法，$ t $在一般的SAS空间中表示为影响参数$ b $的准系列，其系数涉及源镜头距离$ r_s $ r_s $ r_s $ r_s and lens-detector $ r_d $，r_d $，信号速度$ v $ v $ v $，以及非元素扩展系数的元件功能。显示为领先顺序的时间延迟$ΔT$显示由时空质量$ m $，旋转角动量$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ r_d，〜r_d，〜v $和源角度位置$β$。当$β\ ll \ sqrt {am}/r_ {s，d} $时，$Δt$由对旋转$ a $的贡献线性主导。 Modeling the Sgr A* supermassive black hole as a Kerr-Newman black hole, we show that as long as $β\lesssim 1.5\times 10^{-5}$ [$^{\prime\prime}$], then $Δt$ will be able to reach the $\mathcal{O}(1)$ second level, which is well within the time resolution of current GRB, gravitational wave and neutrino天文台。因此，测量这些信号的$ΔT$将使我们能够约束SGR A*的旋转。
Total travel time $t$ and time delay $Δt$ 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 $Δt$ 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 $β\ll \sqrt{aM}/r_{s,d}$, $Δt$ 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 $β\lesssim 1.5\times 10^{-5}$ [$^{\prime\prime}$], then $Δt$ will be able to reach the $\mathcal{O}(1)$ second level, which is well within the time resolution of current GRB, gravitational wave and neutrino observatories. Therefore measuring $Δt$ in GL of these signals will allow us to constrain the spin of the Sgr A*.
