scholarly journals Stability analysis of circular orbits around a charged BTZ black hole spacetime in a nonlinear electrodynamics model via Lyapunov exponents

2021 ◽  
Author(s):  
Shobhit Giri ◽  
Hemwati Nandan ◽  
Lokesh Kumar Joshi ◽  
Sunil D. Maharaj
Keyword(s):  
Black Hole ◽  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Cosmological Constant ◽  
Proper Time ◽  
Btz Black Hole ◽  
Circular Orbits ◽  
Coordinate Time ◽  
Conformally Invariant ◽  
The Stability

We investigate the existence and stability of both the timelike and null circular orbits for a (2 + 1)-dimensional charged BTZ black hole in Einstein-nonlinear Maxwell gravity with a negative cosmological constant. The stability analysis of orbits is performed to study the possibility of chaos in geodesic motion for a special case of black hole so-called conformally invariant Maxwell spacetime. The computations of both proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] are useful to determine the stability of these circular orbits. We observe the behavior of the ratio [Formula: see text] as a function of radius of circular orbits for the timelike case in view of different values of charge parameter. However, for the null case, we calculate only the coordinate time Lyapunov exponent [Formula: see text] as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of [Formula: see text] to angular frequency [Formula: see text], so-called instability exponent as a function of charge [Formula: see text] and parameter related to cosmological constant [Formula: see text] for the particular values of other parameters.

scholarly journals Geodesic stability and quasi normal modes via Lyapunov exponent for Hayward black hole

2020 ◽  
Vol 35 (30) ◽  
pp. 2050249
Author(s):  
Monimala Mondal ◽  
Parthapratim Pradhan ◽  
Farook Rahaman ◽  
Indrani Karar
Keyword(s):  
Black Hole ◽  
Lyapunov Exponent ◽  
Time Scale ◽  
Proper Time ◽  
Normal Modes ◽  
Schwarzschild Black Hole ◽  
Coordinate Time ◽  
Stability And Instability ◽  
The Stability ◽  
Asymptotic Observers

We derive proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] for a regular Hayward class of black hole. The proper time corresponds to [Formula: see text] and the coordinate time corresponds to [Formula: see text], where [Formula: see text] is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as [Formula: see text] for time-like geodesics. In the limit of [Formula: see text] that means for Schwarzschild black hole this ratio reduces to [Formula: see text]. Using Lyapunov 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.

scholarly journals Radial and circular motion of photons and test particles in the Schwarzschild black hole with quintessence and string clouds

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
G. Mustafa ◽  
Ibrar Hussain
Keyword(s):  
Black Hole ◽  
Proper Time ◽  
Schwarzschild Black Hole ◽  
Circular Orbits ◽  
Coordinate Time ◽  
Test Particles ◽  
Close Proximity ◽  
Massive Particles ◽  
Quintessence Field ◽  
Cloud Parameter

AbstractThe null and timelike geodesic motion in the vicinity of the Schwarzschild black hole in the presence of the string cloud parameter a and the quintessence field parameter q is studied. The ranges for both the parameters a and q are determined, which allow the existence of the black hole. In the radial motion of photon, the coordinate time t first decreases with the increasing values of both the parameters a and q and then in the close proximity of the horizon of the black hole, there is a turning point, after which the effect of the quintessence field is just opposite on the time t. For the massive particles, the proper time $$\tau $$ τ decreases with increasing values of the parameter a and increases with increase in the value of the parameter q. In the same case of the massive particles, the coordinate time t decreases with increase in the values of both the parameters a and q. Further, it is found that for test particles, the stable circular orbits exist in this spacetime for small values of both the parameters i.e., for $$0<a\ll 1$$ 0 < a ≪ 1 and $$0<q\ll 1$$ 0 < q ≪ 1 . It is observed that the radii of the null circular orbits increase as the values of the parameters a and q increase. While in the case of the timelike geodesics, the radii of the circular orbits increase as the value of the parameter a increases, and they decrease as the value of the parameter q increases.

scholarly journals Stability of thin-shell wormholes from noncommutative BTZ black hole

2015 ◽  
Vol 24 (05) ◽  
pp. 1550034 ◽  
Author(s):  
Piyali Bhar ◽  
Ayan Banerjee
Keyword(s):  
Black Hole ◽  
Thin Shell ◽  
Static Solution ◽  
Dynamical Analysis ◽  
Energy Conditions ◽  
Btz Black Hole ◽  
Wormhole Throat ◽  
Radial Perturbation ◽  
Thin Shell Wormholes ◽  
The Stability

In this paper, we construct thin-shell wormholes in (2 + 1)-dimensions from noncommutative BTZ black hole by applying the cut-and-paste procedure implemented by Visser. We calculate the surface stresses localized at the wormhole throat by using the Darmois–Israel formalism and we find that the wormholes are supported by matter violating the energy conditions. In order to explore the dynamical analysis of the wormhole throat, we consider that the matter at the shell is supported by dark energy equation of state (EoS) p = ωρ with ω < 0. The stability analysis is carried out of these wormholes to linearized spherically symmetric perturbations around static solutions. Preserving the symmetry we also consider the linearized radial perturbation around static solution to investigate the stability of wormholes which was explored by the parameter β (speed of sound).

scholarly journals Phase transition and holographic in modified Horava–Lifshitz black hole

2017 ◽  
Vol 26 (11) ◽  
pp. 1750138 ◽  
Author(s):  
Kh. Jafarzade ◽  
J. Sadeghi
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Cosmological Constant ◽  
Stability Condition ◽  
Van Der Waals ◽  
Heat Engine ◽  
Fluid Behavior ◽  
Lifshitz Black Hole ◽  
The Stability ◽  
Special Region

In this paper, we take cosmological constant as a thermodynamical pressure and its conjugate quantity as a thermodynamical volume. This expression helps us to investigate the phase transition and holographic heat engine. So, in order to have Van der Waals fluid behavior in Horava–Lifshitz (HL) black hole, we modified the solution of such black hole with some cosmology ansatz. Also from holographic heat engine, we obtain Carnot efficiency for the HL black hole. The phase transition of the system lead us to investigate the stability condition for the corresponding black hole. In that case, we show that the stability exist only in special region of black hole.

scholarly journals Deflection of light around a rotating BTZ black hole

2020 ◽  
Vol 35 (39) ◽  
pp. 2050323
Author(s):  
Shubham Kala ◽  
Hemwati Nandan ◽  
Prateek Sharma
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Test Particle ◽  
Gravitational Lensing ◽  
Critical Parameters ◽  
Btz Black Hole ◽  
Bending Angle ◽  
Retrograde Motion ◽  
Test Particles ◽  
Dimensional Gravity

We present a detailed study of gravitational lensing around a rotating Bañados–Teitelboim–Zanelli (BTZ) black hole in (2 + 1)-dimensional gravity. The study of orbits for massless test particle around this BH spacetime is performed to describe the nature of cosmological constant in lower dimensions. We study the effect of cosmological constant on the photon orbit in view of other critical parameters. The bending angle of light is studied in view of different values of cosmological constant for direct and retrograde motion of test particles. It is being observed that the bending angle slightly decreases as the value of cosmological constant increases in the negative region.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

scholarly journals Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 841 ◽  
Author(s):  
Anton Sheykin ◽  
Dmitry Solovyev ◽  
Sergey Paston
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Isometric Embedding ◽  
Flat Space ◽  
Ambient Space ◽  
Spherically Symmetric ◽  
Btz Black Hole ◽  
3 Dimensional ◽  
Negative Cosmological Constant

We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of d-dimensional Schwarzschild-AdS black hole in a flat ( d + 3 ) -dimensional ambient space.

Effects of electromagnetic field on the motion of particles in dyonic Reissner–Nordström black hole

2017 ◽  
Vol 26 (09) ◽  
pp. 1750091 ◽  
Author(s):  
M. Sharif ◽  
Sehrish Iftikhar
Keyword(s):  
Black Hole ◽  
Electromagnetic Field ◽  
Lyapunov Exponent ◽  
Circular Orbit ◽  
Center Of Mass ◽  
Mass Energy ◽  
Center Of Mass Energy ◽  
Stable Circular Orbit ◽  
The Stability ◽  
Dynamics Of Particles

This paper explores dynamics of particles in the combined gravitational and electromagnetic fields of the dyonic Reissner–Nordström background. We discuss possibilities for the particle escape to infinity at inner most stable circular orbit. We study the stability of orbit through Lyapunov exponent and the effective force on particle. The collision of particles is investigated through the center of mass energy near the horizon of black hole. Finally, we compare our results with the motion of particles around Schwarzschild and Reissner–Nordström black hole. We conclude that charge of the black hole has a strong effect on the motion of particles.

scholarly journals QUASINORMAL MODES AND STABILITY ANALYSIS FOR Z = 4 TOPOLOGICAL BLACK HOLE IN 4 + 1-DIMENSIONAL HORAVA–LIFSHITZ GRAVITY

2013 ◽  
Vol 22 (02) ◽  
pp. 1350007 ◽  
Author(s):  
RAMÓN BECAR ◽  
P. A. GONZÁLEZ ◽  
YERKO VÁSQUEZ
Keyword(s):  
Black Hole ◽  
Stability Analysis ◽  
Imaginary Part ◽  
Quasinormal Modes ◽  
The Stability ◽  
Scalar Perturbations

We study the stability of z = 4 topological black hole in 4 + 1-dimensional Horava–Lifshitz gravity against scalar perturbations by analyzing the quasinormal modes (QNMs). It is possible to distinguish two cases for which the black hole is stable. The first one occurs when p + Q > 0 and QNMs are characterized by a real and imaginary part, meaning that the field has oscillatory modes but with Im (ω) < 0; therefore, it is stable. While in the second case p + Q < 0, QNMs are purely imaginary ( Im (ω) < 0) and then absolutely damped.

scholarly journals QUASINORMAL MODES AND STABILITY ANALYSIS FOR FOUR-DIMENSIONAL LIFSHITZ BLACK HOLE

2012 ◽  
Vol 21 (06) ◽  
pp. 1250054 ◽  
Author(s):  
P. A. GONZÁLEZ ◽  
JOEL SAAVEDRA ◽  
YERKO VÁSQUEZ
Keyword(s):  
Black Hole ◽  
Stability Analysis ◽  
Quasinormal Modes ◽  
Dynamical Exponent ◽  
Four Dimensions ◽  
Lifshitz Black Hole ◽  
The Stability ◽  
Scalar Perturbations

We study the Lifshitz black hole in four dimensions with dynamical exponent z = 2 and we calculate analytically the quasinormal modes of scalar perturbations. These quasinormal modes allow to study the stability of the Lifshitz black hole and we have obtained that Lifshitz black hole is stable.

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