We consider test particle motion in a gravitational field generated by a homogeneous circular ring placed in $n$-dimensional Euclidean space. We observe that there exist no stable stationary orbits in $n=6, 7, \ldots, 10$ but exist in $n=3, 4, 5$ and clarify the regions in which they appear. In $n=3$, we show that the separation of variables of the Hamilton-Jacobi equation does not occur though we find no signs of chaos for stable bound orbits. Since the system is integrable in $n=4$, no chaos appears. In $n=5$, we find some chaotic stable bound orbits. Therefore, this system is nonintegrable at least in $n=5$ and suggests that the timelike geodesic system in the corresponding black ring spacetimes is nonintegrable.
Newtonian gravitational potential sourced by a homogeneous circular ring in arbitrary dimensional Euclidean space takes a simple form if the spatial dimension is even. In contrast, if the spatial dimension is odd, it is given in a form that includes complete elliptic integrals. In this paper, we analyze the dynamics of a freely falling massive particle in its Newtonian potential. Focusing on circular orbits on the symmetric plane where the ring is placed, we observe that they are unstable in 4D space and above, while they are stable in 3D space. The sequence of stable circular orbits disappear…
In this paper, we consider a charged particle moves around a Weakly Magnetized Kerr-Newman black hole. We first study its circular motion with a detailed analysis in the innermost stable circular orbits(ISCO). Then the dynamics of a particle, kicked out from the circular orbit, is also explored. The final states can be characterized into three different types: bound motion, captured by black hole or escape to spatial infinity. The respective trajectories are shown, and are mainly determined by the energy of a particle after a kick and the initial condition, in which we use Basins of attraction…
We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.
We consider scattering and capture of circular cosmic strings by a Schwarzschild black hole. Although being a priori a very simple axially symmetric two-body problem, it shows all the features of chaotic scattering. In particular, it contains a fractal set of unstable periodic solutions; a so-called strange repellor. We study the different types of trajectories and obtain the fractal dimension of the basin-boundary separating the space of initial conditions according to the different asymptotic outcomes. We also consider the fractal dimension as a function of energy, and discuss the transition…
Within the framework of Bonnor's exact solution describing a massive magnetic dipole, we study the motion of neutral and electrically charged test particles. In dependence on the Bonnor spacetime parameters, we determine regions enabling the existence of stable circular orbits confined to the equatorial plane and of those levitating above the equatorial plane. Constructing Poincaré surfaces of section and recurrence plots, we also investigate the dynamics of particles moving along general off-equatorial trajectories bound in effective potential wells forming around the stable circular orbits. …
Yes, if the universe has compact topology. Inflation is currently the most elegant explanation of why the universe is old, large, nearly flat, homogeneous on large scales and structured on small scales. One of the weaknesses of the inflationary paradigm is the problem of initial conditions for inflation: the pre-inflationary universe must be somewhat old, somewhat large and somewhat homogeneous. These initial condition requirements are even more severe in Omega < 1 inflationary models: if the universe does not inflate enough to appear flat, then it does not inflate enough to appear homogeneous…
We demonstrate that geodesics in exact vacuum Kundt gravitational waves may exhibit a highly complicated behaviour. In fact, as in the previously studied case of non-homogeneous pp-waves, for specific choices of the structural function the motion appears to be genuinely chaotic. This fact is demonstrated by the fractal method.
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass monopole/spin-induced quadrupole interaction terms. In the case of both quasi-circular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasi-circular orbits, we find no chaotic behavior for black holes with total mass 10 - 40 solar masses when initially at a separation cor…
We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct "outcomes" (channels to infinity) are identified, and it is shown that the boundary between different outcomes has a fractal structure. This seems to be the first example of chaos in exact radiative spacetimes.
Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Institute of Fundamental and Applied Research, National Research University TIIAME（TIIAME国立研究型大学基础与应用研究所）；Tashkent State Technical University（塔什干国立技术大学）
We show that homogeneous and isotropic cosmological models with radiation and scalar field have, in general, two possible chaotic exits to inflation. These models may describe the early stages of inflation. The central point of our analysis is based on the possible existence of one or two saddle-centers points in the phase space of the models.
We demonstrate chaotic behavior of timelike, null and spacelike geodesics in non-homogeneous vacuum pp-wave solutions. This seems to be the first known example of a chaotic motion in exact radiative spacetime.
We investigate the chaotic behavior of a circular test string in the Lifshitz spacetimes considering the critical exponent $z$ as an external control parameter. It is demonstrated that two primary tools to observe chaos in this system are Poincaré section and Lyapunov exponent. Finally, the numerical result shows that if $z=1$, the string dynamics is regular, while in a case slightly larger than $z=1$, the dynamics can be irregular and chaotic.
Probing Quantum Gravity through Chaotic Orbits and Strong-Field Effects in Kerr Black Holes Embedded in Perfect Fluid Dark Matter
The Institute of Mathematical Sciences, C.I.T. Campus（泰米鲁纳德邦金奈塔拉马尼 CIT 校区的数学科学研究所）；Khazar University（阿塞拜疆巴库的哈萨尔大学）；University of Mazandaran（伊朗巴巴萨尔的马赞达兰大学）；Virtual University of Pakistan（巴基斯坦拉合尔的虚拟大学）；Hemwati Nandan Bahuguna Garhwal University（印度北阿坎德邦斯里纳加的赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Harbin Institute of Technology（中国哈尔滨的哈尔滨工业大学）；Zhejiang Normal University（中国金华的浙江师范大学）
We consider spatially homogeneous models in Hořava-Lifshitz (HL) gravity that perturbs General Relativity (GR) by a parameter $v\in (0,1)$ such that GR occurs at $v=1/2$. We prove that the induced Kasner map is chaotic for a broad class of modified HL gravity models, when $v\in (0,1/2)$, despite the fact that the Kasner map is multivalued in such subcritical regime.
A charged particle kicked from an initial circular orbit around a weakly magnetized Schwarzschild black hole undergoes transient chaotic motion before either getting captured by the black hole or escaping upstream or downstream with respect to the direction of the magnetic field. These final states form basins of attraction in the space of initial states. We provide a detailed numerical study of the basin structure of this initial state space. We find it to possess the peculiar Wada property: each of its basin boundaries is shared by all three basins. Using basin entropy as a measure, we show …
A spinning test particle around a Schwarzschild black hole shows a chaotic behavior, if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion is not always enhance the energy emission …
Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small electric charge due to interplay of plasma processes and photoionization. In particular, we employ an exact solution describing the massive magnetic dipole and we identify the regions of stable mot…
A chaotic model of the early universe within the framework of the singularity-free solutions of Einstein's equation is suggested. The evolution of our universe at its early stage, starting out as a small domain of the parent universe, is governed by the dynamics of a classical scalar field $ϕ$ . If in any such domain, larger than Planck length,$\dot ϕ$ happens to be very large,$ϕ$ may develop a dominant inhomogeneous mode,leading to an anisotropic inflation of the universe. The particle $ϕ$ is coupled to other particles, which are produced copiously after inflation and these thermalize leading…
We discuss charged particles motion in a spacetime of a weakly magnetized static non-rotating black hole. We study under which conditions a charged particle originally revolving around the black hole at a circular orbit after being kicked by another particle or photon can escape to infinity. We determine the escape velocity for particles at the innermost stable circular orbits and discuss the properties of particles moving with near-critical velocity. We show that in a general case such a motion is chaotic.
