论文标题
通过Lyapunov指数Hayward Black Hole的地球稳定性和准正常模式
Geodesic stability and Quasi normal modes via Lyapunov exponent for Hayward Black Hole
论文作者
论文摘要
我们得出适当的时间lyapunov指数$（λ_{p}）$和坐标时间lyapunov exponent $（λ_{c}）$，用于常规的黑洞Hayward类。正确的时间对应于$τ$，坐标时间对应于$ t $。 $ t $由渐近观察者用于海沃德黑洞和Schwarzschild黑洞的特殊情况。 我们将它们的比率计算为$ \ frac {λ_{p}} {λ_{c}} = \ frac {（r_σ^{3} + 2 l^{2} m）} {\ sqrt {\ sqrt { R_σ^{5}}}} $用于类似时间的大地测量。在$ l = 0 $的限制中，这意味着Schwarzschild黑洞该比率降低到$ \ frac {λ_{p}} {λ_{C}} = \ sqrt {\ frac {\ frac {r_σ}} {（r_σ-3m）}} $。使用Lyponuov指数，我们研究了赤道圆形测量学的稳定性和不稳定性。通过评估不稳定时间尺度的lyapunov指数，我们表明，在Eikonal限制下，准正常模式的实际和虚构部分〜（QNMS）由零循环测量学的频率和不稳定性时间尺度指定。 此外，我们讨论了这类黑洞的不稳定光子球和阴影半径。
We derive proper-time Lyapunov exponent $(λ_{p})$ and coordinate-time Lyapunov exponent $(λ_{c})$ for a regular Hayward class of black hole. The proper-time corresponds to $τ$ and the coordinate time corresponds to $t$. Where $t$ is measured by the asymptotic observers both for for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as $\frac{λ_{p}}{λ_{c}} = \frac{(r_σ^{3} + 2 l^{2} m )}{\sqrt{(r_σ^{2} + 2 l^{2} m )^{3}- 3 m r_σ^{5}}}$ for time-like geodesics. In the limit of $l=0$ that means for Schwarzschild black hole this ratio reduces to $\frac{λ_{p}}{λ_{c}} = \sqrt{\frac{r_σ}{(r_σ-3 m)}}$. Using Lyponuov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time-scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes~(QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.
