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Stability analysis of geodesics and quasinormal modes of a dual stringy black hole via Lyapunov exponents
General Relativity and Gravitation ( IF 2.8 ) Pub Date : 2021-08-05 , DOI: 10.1007/s10714-021-02845-9
Shobhit Giri 1 , Hemwati Nandan 1, 2
Affiliation  

We investigate the stability of both timelike as well as null circular geodesics in the vicinity of a dual (3+1) dimensional stringy black hole (BH) spacetime by using an excellent tool so-called Lyapunov exponent. The proper time (\(\tau \)) Lyapunov exponent (\(\lambda _{p}\)) and coordinate time (t) Lyapunov exponent (\(\lambda _{c}\)) are explicitly derived to analyze the stability of equatorial circular geodesics for the stringy BH spacetime with electric charge parameter (\(\alpha \)) and magnetic charge parameter (Q). By computing these exponents for both the cases of BH spacetime, it is observed that the coordinate time Lyapunov exponent of magnetically charged stringy BH for both timelike and null geodesics are independent of magnetic charge parameter (Q). The variation of the ratio of Lyapunov exponents with radius of timelike circular orbits (\(r_{0}/M\)) for both the cases of stringy BH are presented. The behavior of instability exponent for null circular geodesics with respect to charge parameters (\(\alpha \) and Q) are also observed for both the cases of BH. Further, by establishing a relation between quasinormal modes (QNMs) and parameters related to null circular geodesics (like angular frequency and Lyapunov exponent), we deduced the QNMs (or QNM frequencies) for a massless scalar field perturbation around both the cases of stringy BH spacetime in the eikonal limit. The variation of scalar field potential with charge parameters and angular momentum of perturbation (l) are visually presented and discussed accordingly.



中文翻译:

基于李雅普诺夫指数的双弦黑洞测地线和准正规模态稳定性分析

我们通过使用称为 Lyapunov 指数的优秀工具研究了双 (3+1) 维弦状黑洞 (BH) 时空附近的类时和零圆测地线的稳定性。适当的时间(\(\tau \))李雅普诺夫指数(\(\lambda _{p}\))和坐标时间(t)李雅普诺夫指数(\(\lambda _{c}\))被明确导出以进行分析具有电荷参数 ( \(\alpha \) ) 和磁荷参数 ( Q)。通过为 BH 时空的两种情况计算这些指数,可以观察到,对于类时和零测地线,磁荷细 BH 的坐标时间李雅普诺夫指数与磁荷参数 ( Q )无关。给出了两种弦BH情况下Lyapunov指数的比值随类时圆轨道半径( \(r_{0}/M\) )的变化。相对于电荷参数 ( \(\alpha \)Q 的零圆形测地线的不稳定指数行为) 也观察到 BH 的两种情况。另外,通过建立与空圆形的测地线(如角频率和Lyapunov指数)拟正规模式(QNMs)和参数之间的关系,我们推导出QNMs(或QNM频率)用于围绕无质量标量场扰动拉丝BH的情况下时空在 eikonal 极限。标量场势随电荷参数和扰动角动量(l)的变化被直观地呈现和讨论。

更新日期:2021-08-10
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