scholarly journals Light rings of five-dimensional geometries

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
M. Bianchi ◽  
D. Consoli ◽  
A. Grillo ◽  
J. F. Morales
Keyword(s):  
Lyapunov Exponent ◽  
Large Family ◽  
Chaotic Behaviour ◽  
Mass Center ◽  
Time Decay ◽  
Maxwell Theory ◽  
Dimensional Solution ◽  
Naked Singularities ◽  
Five Dimensions ◽  
Light Ring

Abstract We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the five-dimensional solution. We find that a light ring of unstable photon orbits surrounding the mass center is always present, independently of the existence of a horizon or singularity. We compute the Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the ‘photon-sphere’ and the time decay of ring-down modes dominating the response of the geometry to perturbations at late times. We show that, for geometries free of naked singularities, the Lyapunov exponent is always bounded by its value for a Schwarzschild BH of the same mass.

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

scholarly journals Minimal surfaces and generalized Einstein–Maxwell-dilaton theory

2019 ◽  
Vol 34 (12) ◽  
pp. 1950061
Author(s):  
M. Butler ◽  
A. M. Ghezelbash
Keyword(s):  
Cosmological Constant ◽  
Physical Properties ◽  
Minimal Surfaces ◽  
Higher Dimensions ◽  
Coupling Constants ◽  
Dilaton Field ◽  
Coupling Constant ◽  
Maxwell Theory ◽  
Five Dimensions ◽  
Cosmological Solutions

We present novel classes of nonstationary solutions to the five-dimensional generalized Einstein–Maxwell-dilaton theory with cosmological constant, in which the Maxwell’s field and the cosmological constant couple to the dilaton field. In the first class of solutions, the two nonzero coupling constants are different, while in the second class of solutions, the two coupling constants are equal to each other. We find consistent cosmological solutions with positive, negative or zero cosmological constant, where the cosmological constant depends on the value of one coupling constant in the theory. Moreover, we discuss the physical properties of the five-dimensional solutions and the uniqueness of the solutions in five dimensions by showing the solutions with different coupling constants cannot be uplifted to any Einstein–Maxwell theory in higher dimensions.

Periodic and chaotic behaviour in a reduction of the perturbed Korteweg-de Vries equation

1994 ◽  
Vol 445 (1923) ◽  
pp. 1-21 ◽  
Keyword(s):  
Lyapunov Exponent ◽  
Vries Equation ◽  
Period Doubling ◽  
Homoclinic Orbits ◽  
Dynamical Behaviour ◽  
Chaotic Behaviour ◽  
Subharmonic Bifurcations ◽  
Melnikov Functions ◽  
De Vries ◽  
Period Doubling Bifurcations

The dynamical behaviour of a reduction of the forced (and damped) Korteweg-de Vries equation is studied numerically. Chaos arising from subharmonic instability and homoclinic crossings are observed. Both period-doubling bifurcations and the Melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour, here characterised by a positive Lyapunov exponent. Supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits, and their behaviour under perturbation using Melnikov functions.

scholarly journals Linearly Coupled Anharmonic Oscillators and Integrability

1987 ◽  
Vol 40 (5) ◽  
pp. 587
Author(s):  
W-H Steeb ◽  
JA Louw ◽  
CM Villet
Keyword(s):  
Lyapunov Exponent ◽  
Anharmonic Oscillator ◽  
First Integrals ◽  
Chaotic Behaviour ◽  
Painlevé Test ◽  
Anharmonic Oscillators ◽  
One Dimensional

The Painleve test for a linearly coupled anharmonic oscillator is performed. We show that this system does not pass the Painleve test. This suggests that this system is not integrable. Moreover, we apply Ziglin's (1983) theorem which provides a criterion for non-existence of first integrals besides the Hamiltonian. Calculating numerically the maximal one-dimensional Lyapunov exponent, we find regions with positive exponents. Thus, the system can show chaotic behaviour. Finally we compare our results with the quartic coupled anharmonic oscillator.

scholarly journals Black holes with scalar hair in Einstein–Gauss–Bonnet gravity

2016 ◽  
Vol 25 (07) ◽  
pp. 1650084 ◽  
Author(s):  
Y. Brihaye ◽  
L. Ducobu
Keyword(s):  
Black Holes ◽  
Angular Velocity ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Large Family ◽  
Scalar Fields ◽  
Regular Solutions ◽  
Five Dimensions ◽  
Bonnet Gravity ◽  
Scalar Hair

The Einstein–Gauss–Bonnet gravity in five dimensions is extended by scalar fields and the corresponding equations are reduced to a system of nonlinear differential equations. A large family of regular solutions of these equations is shown to exist. Generically, these solutions are spinning black holes with scalar hairs. They can be characterized (but not uniquely) by an horizon and an angular velocity on this horizon. Taking particular limits, the black holes approach boson star or become extremal, in any case the limiting configurations remain hairy.

scholarly journals Image of the thin accretion disk around compact objects in the Einstein–Gauss–Bonnet gravity

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Galin Gyulchev ◽  
Petya Nedkova ◽  
Tsvetan Vetsov ◽  
Stoytcho Yazadjiev
Keyword(s):  
Black Holes ◽  
Accretion Disk ◽  
Physical Mechanism ◽  
Compact Object ◽  
Ring Structure ◽  
Compact Objects ◽  
Schwarzschild Black Hole ◽  
Naked Singularities ◽  
Bonnet Gravity ◽  
Light Ring

AbstractWe study the optical appearance of a thin accretion disk around compact objects within the Einstein–Gauss–Bonnet gravity. Considering static spherically symmetric black holes and naked singularities we search for characteristic signatures which can arise in the observable images due to the modification of general relativity. While the images of the Gauss–Bonnet black holes closely resemble the Schwarzschild black hole, naked singularities possess a distinctive feature. A series of bright rings are formed in the central part of the images with observable radiation $$10^3$$ 10 3 times larger than the rest of the flux making them observationally significant. We elucidate the physical mechanism, which causes the appearance of the central rings, showing that the image is determined by the light ring structure of the spacetime. In a certain region of the parametric space the Gauss–Bonnet naked singularities possess a stable and an unstable light ring. In addition the gravitational field becomes repulsive in a certain neighbourhood of the singularity. This combination of features leads to the formation of the central rings implying that the effect is not specific for the Einstein–Gauss–Bonnet gravity but would also appear for any other compact object with the same characteristics of the photon dynamics.

scholarly journals Evidence for nonlinear and chaotic behaviour in pulsar spin-down rates

2012 ◽  
Vol 8 (S291) ◽  
pp. 495-495
Author(s):  
Andrew Seymour ◽  
Duncan Lorimer
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Nonlinear Equations ◽  
Strange Attractor ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Structural Information ◽  
Chaotic Behaviour ◽  
Present Evidence

AbstractWe present evidence for chaotic dynamics in pulsar spin-down rates originally measured by Lyne et al. (2010). Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence for a strange attractor in the time series of frequency derivative for each pulsar. Our measurements of correlation dimension and Lyapunov exponent show, particularly in the case of PSR B1828-11, that the underlying behavior appears to be driven by a strange attractor with approximately three governing nonlinear equations.

scholarly journals NAKED SINGULARITIES IN HIGHER DIMENSIONAL GRAVITATIONAL COLLAPSE

2003 ◽  
Vol 12 (07) ◽  
pp. 1255-1263 ◽  
Author(s):  
ASIT BANERJEE ◽  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Dimensional Space ◽  
Naked Singularity ◽  
Space Time ◽  
Naked Singularities ◽  
Five Dimensions ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Five Dimension

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

scholarly journals TOPOLOGICAL BLACK HOLES OF (n+1)-DIMENSIONAL EINSTEIN–YANG–MILLS GRAVITY

2010 ◽  
Vol 25 (18) ◽  
pp. 1507-1519 ◽  
Author(s):  
N. BOSTANI ◽  
M. H. DEHGHANI
Keyword(s):  
Black Holes ◽  
Naked Singularity ◽  
De Sitter ◽  
Negative Mass ◽  
Dimensional Solution ◽  
Five Dimensions ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Em Theory ◽  
Metric Function

We present the topological solutions of Einstein gravity in the presence of a non-Abelian Yang–Mills field. In (n+1) dimensions, we consider the SO (n(n-1)/2-1, 1) semisimple group as the Yang–Mills gauge group, and introduce the black hole solutions with hyperbolic horizon. We argue that the four-dimensional solution is exactly the same as the four-dimensional solution of Einstein–Maxwell gravity, while the higher-dimensional solutions are new. We investigate the properties of the higher-dimensional solutions and find that these solutions in five dimensions have the same properties as the topological five-dimensional solution of Einstein–Maxwell (EM) theory although the metric function in five dimensions is different. But in six and higher dimensions, the topological solutions of EYM and EM gravities with non-negative mass have different properties. First, the singularity of EYM solution does not present a naked singularity and is spacelike, while the singularity of topological Reissner–Nordström solution is timelike. Second, there are no extreme six or higher-dimensional black holes in EYM gravity with non-negative mass, while these kinds of solutions exist in EM gravity. Furthermore, EYM theory has no static asymptotically de Sitter solution with non-negative mass, while EM gravity has.

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