Strong Gravitational Lensing Of Black Holes And Quantum Chaos In Two-photon Dicke Model

Gravitational lensing is caused by the deflection of the light ray as photons pass close to the celestial body with strong gravitational field,such as a compact and massive star.Black hole is a kind of supermassive compact objects predicted by general relativity,whose gravitational field are so strong that nothing,not even light emitted by themselves can escape.Gravitational lensing has been used to identify black hole and examine various gravity theories.And then,it has been applied extensively in cosmology,astronomy and black hole physics.Classical chaos is usually related to the exponential separation of trajectories.In quantum mechanics,the conjugate observations for a quantum state,such as position and momentum,cannot have certain values at the same time due to the uncertainty principle.This essential difference makes it impossible to define quantum chaos directly similar to classical chaos.On the other hand,the universality of the correspondence between quantum entanglement and chaos has been facing a great challenge in the few body quantum system.One of the goals of studying quantum chaos is to establish the corresponding principle between chaotic dynamics in classical limit and quantum dynamics for a quantum system.In this paper,we have studied firstly the strong gravitational lensing and the time delay effect in the Konoplya-zhidenko rotating black hole spacetime and in the Kerr black hole spacetime with the coupling between the photon and Weyl tensor.And then,we studied the chaotic behaviors in both single-photon and double-photon Dicke models,and found that the corresponding relationship between entanglement and classical phase space can be improved by increasing the system energy.In the first chapter,we make a brief introduction on the gravitational lensing and quantum chaos.In the second chapter,we have studied the strong gravitational lensing in a Konoplya-zhidenko rotating non-Kerr spacetime with an extra deformation parameter.It is shown that the condition of existence of horizons is not inconsistent with that of the circular photon orbit.Moreover,the deflection angle of the light ray near the weakly naked singularity covered by the marginally circular orbit diverges logarithmically in the strong-field limit.In the case of the completely naked singularity,the defection angle near the singularity tends to a certain finite value,whose sign depends on the rotation parameter and the deformation parameter.Modeling the supermassive central object of the Milk Way Galaxy as a KonoplyaZhidenko rotating non-Kerr compact object,we estimated the numerical values of observables for the strong gravitational lensing including the time delay between two relativistic images.In the third chapters,we present the equation of motion for the photon coupled to a Weyl tensor in a Kerr black hole spacetime and find that black hole rotation makes propagation of the coupled photons more complicated,which brings about some newfeatures for physical quantities.(i)There is a critical value of the coupling parameter for existence of the marginally circular photon orbit outside the event horizon,which depends on the rotation parameter of the black hole and the polarization direction of the photons.(ii)As the value of the coupling parameter nears the critical value,we find that the marginally circular photon orbit for the retrograde photon increases with the rotation parameter,which modifies a common feature of the marginally circular photon orbit in a rotating black hole spacetime since it always decreases monotonously with the rotation parameter in the case without Weyl coupling.With the supermassive central object in our Galaxy,we also estimated the numerical values of the observables including time delays between the relativistic images in the strong gravitational lensing as the photons couple to Weyl tensor.In the forth chapter,we have studied entanglement entropy and Husimi Q distribution to explore chaos in the quantum two-photon Dicke model and singlephoton Dicke model.With the increase of the energy of a system,it is shown that the linear entanglement entropy of coherent state prepared in the classical chaotic and regular regions becomes more distinguishable,and the corresponding relationship between the distribution of time-averaged entanglement entropy and the classical Poincar?e section has clearly been improved.Moreover,Husimi Q distribution for the initial states corresponding to the points in the chaotic region in the higher-energy system disperses more quickly than that in the lower-energy system.Our results imply that higher system energy has contributed to distinguishing between the chaotic and regular behavior in the quantum two-photon Dicke model.Finally,we present a summary and make some prospects for the investigation of strong gravitational lensing and quantum chaos.