Geodesic stability and Quasi normal modes via Lyapunov exponent for Hayward Black Hole

Abstract

We derive proper-time Lyapunov exponent $({\lambda }_p)$ and coordinate-time Lyapunov exponent $({\lambda }_c)$ for a regular Hayward class of black hole. The proper-time corresponds to $\tau$ 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 $\frac{{\lambda }_p}{{\lambda }_c}=\frac{(r_{\sigma }^3+2l^{2}m)}{\sqrt{(r_{\sigma }^2+2l^{2}m{)}^3-3m{r}_{\sigma }^5}}$ for time-like geodesics. In the limit of $l=0$ that means for Schwarzschild black hole this ratio reduces to $\frac{{\lambda }_p}{{\lambda }_c}=\sqrt{\frac{r_{\sigma }}{(r_{\sigma }-3m)}}$. 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.

To appear in Mod.Phys.Lett.A, 19 pages and 6 figures

References in corpus (9)

• Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
• Notes on non-singular models of black holes
• Are eikonal quasinormal modes linked to the unstable circular null geodesics?
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• The high-energy collision of two black holes
• Circular motion of neutral test particles in Reissner-Nordström spacetime
• Black Hole Mergers and Unstable Circular Orbits
• Relaxations of perturbations of spacetimes in general relativity coupled to nonlinear electrodynamics
• Relativistic chaos is coordinate invariant

Cited by in corpus (5)

• Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent
• Lyapunov exponent ISCO and Kolmogorov Senai entropy for Kerr Kiselev black hole
• Stability Analysis of Geodesics and Quasinormal Modes of a Dual Stringy Black Hole Via Lyapunov Exponents
• Lyapunov exponents and geodesic stability of Schwarzschild black hole in the non-commutative gauge theory of gravity
• Gravitational decoupling and regular hairy black holes: Geodesic stability, quasinormal modes, and thermodynamic properties