Researches On Strong Gravitational Lensing?black Hole?Dark Matter?Dark Energy And Related Problems

The study of black hole,dark matter,dark energy,gravitational lensing and quantum gravity are all the most hottest topics of astronomy,astrophysics,theoretical physics.Quantum gravity,a unification of gravity and quantum mechanism,has led many hints that the fundamental description of spacetime should not be based on the familiar concept of a classical smooth geometry,but on a new,somehow quantized picture,in which this distance scale is always named as“the minimum measurable length”.At present,the minimum measurable length is always expected to be the Planck length.Up to now,we still stay in the course of seeking a perfect theory of quantum gravity in the theories to obtain the quantization of gravity.In view of this,the effective theoretical model of quantum gravity attracts more and more attentions of people's eyes,where the main deformed models including:?a?.Lorenz Invariance Violation?LIV?;?b?.GeneralizedUncertaintyPrinciple?GUP?.Obviously,ModifiedDispersion Relation?MDR?is the simplest kinematic framework of Lorenz Invariance Violation,and it also can be found in the Doubly Special Relativity?DSR?.Combined with those facts,it is very important and meaningful for us to employing the Lorentz-invariance violation class of Dispersion Relation,to phenomenologically study the effect of quantum gravity in balck hole.Based on the gravitational lensing,the thermodynamic evolution of black hole and the effective theory of quantum gravity,the main content of this paper can be organized as,1.Based on the strong field limit approach,we first studied the strong gravitational lensing both from a spherical symmetry spacetime in Einstein-Proca theory and a Brane-World black hole spacetime,then we obtained the strong field limit coefficients and deflection angle.It turns out that,A?In Einstein-Proca theory,we found that the deflection angle is always diverge as a form of logarithm,which extend the field limit approach perfectly;B?The dark matter increase the strength of gravitational field,and so,the strong fields limit coefficients,the deflection angle,the position of image and the angular separation increased with the dark matter parameterb.Hence,one can see that the gravitational lensing can be regarded as an indirect way for seeking the property of dark matter.2.Our study shows that,A?For the different spin particles,we find that the Hamilton-Jacobi equation can be used to study the tunneling behavior of any particle in curved space-time.This means the Hamilton-Jacobi equation is a basic particle equation of motion.B?Using the Hamilton-Jacobi equation,we studied the Hawking radiation from a spherically symmetric black hole with dark matter.C?By employing the Hamilton-Jacobi equation,we also study the quantum tunneling of a charged spherically symmetric Kinnersly black hole.The results show that,the Hamilton-Jacobi equation is very convenient to study the quantum tunneling behavior of arbitrary spin particles.Furthermore,compared with the previous work,we can obviously see that it is more convenient to study tunneling radiation by using the Hamilton-Jacobi equation.Especially for the fermion's tunneling,since there is no need to construct the complex Gamma matrix by a tedious calculation,which greatly reduces the workload,it is better to carry out creative research in depth.3.Using the oscillating velocity of black hole horizon,we studied black hole spectroscopy from a spherically symmetric spacetime in different gravity frames?including Einstein gravity,Einstein-Gauss-Bonnet?EGB?gravity,Ho?ava-Lifshitz?HL?gravity?.A?In the different coordinates,we once again examine the fact that,in different types?Schwarzschild and Painlevé?of coordinates as well as in different gravity frames,the adiabatic invariantis???canonically invariant.B?In different gravity frames,using oscillating velocity of the black hole horizon,we find that the entropy spectrum has the same form,but in EGB and HL gravity,the spacing of the area spectrum is not equidistant obviously.C?we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable,but the horizon area is only an adiabatic invariant.4.We first confirm that,the LIV-DR should be acted as a second generation of Planck length suppressed dispersion relation,if it really originates from quantum gravity.Based on this relation,we obtained the quantum-gravity-induced Dirac equation in the curved spacetime.According to this modified Dirac equation,we first study the fermions'tunneling radiation from Schwarzschild black hole and R-N black hole.The results in this paper shows that the real Hawking temperature is not only related the black hole parameter?ie.,black hole mass M and electric charge Q?,but also related to quantum parameterl _p?the energywand the mass m of emitted particles.5.The study further shows that:A?the corrected temperature is higher than that of original value,quantum gravity speed up the evaporation of black hole,but black hole would never evaporate completely,it would stop to evaporate when Hawking temperature reach to some certain maximum value,and then left remnant value of temperatureT_{re m}?massM_rem?entropyS_remat the final stage of black hole.B?In addition,we obtained the singular mass and critical mass,which can be regarded as a solution of singularity problems of black hole.C?Compared the LIV-DR induced and the GUP induced effects in black hole thermodynamics,it turns out that,in the same model-dependent parameters the LIV-DR acts as a more suitable candidate.D?Meanwhile,in the context of LIV-DR,it turns out that,Hawking radiation as quantum tunneling is still a process of entropy conservation.That is to say,black hole information loss dose not occur,and the unitarity of quantum mechanics is also conserved.At last of this paper,we give a brief description with respect to the dark matter and dark energy,in which some research progress and prospect are presented.The main content in this paper is part of the hottest spots of the international research about strong gravitational lensing?black hole?dark matter?dark energy and quantum gravity.For example,based on the LIV-DR,we discuss the effects of quantum gravity on black hole thermodynamics.At present,the quantum gravity theory has not yet been formed,therefore it is very interesting and meaningful for us to study the effect of quantum gravity under the background of phenomenal model.And,we have a good reason to believe that those studies would provide a new reference for the forthcoming quantum gravity.