Research On The Quantum Effects Of Black Holes And The Related Problems Of Strong Gravitational Field In Curved Spacetime

The research of this thesis involves the hot topics related to black hole information loss paradox,semiclassical quantization,gravity correction and holographic properties.The study of quantum effects of black holes mainly include the quantization of black hole horizon area and the quantum tunneling radiation under the influence of the generalized uncertainty principle(GUP).The related problems of strong gravitational field in curved spacetime include the following two aspects.On one hand,considering the quantum gravitational effect caused by GUP in curve spacetime of strong gravitational field formed by Finsler black holes,we study the related thermodynamic properties of Finsler black holes under modified gravity.On the other hand,in the framework of holography,we discuss the holographic Van der Waals phase transition of high-dimensional AdS hairy black holes with scalar field hair effect in curved spacetime of a strong gravitational field.The specific content and main results are as follows:1.By modifying the adiabatic invariant proposed by Majhi and Vagenas,we derive a new adiabatic invariant for axisymmetric black holes,that is,covariant adiabatic invariant.Thus,the horizon area of a Kerr black hole is quantized in different coordinates.The result shows that in these coordinates,the horizon area is all(35)A(28)8?l_p~2,and the area spectrum is equidistant spacing,which confirms the initial proposal of Bekenstein.It is noteworthy that the covariant adiabatic invariant gives the covariant result for a black hole spectroscopy in different coordinates.Especially,in contrast to the quasinormal mode method,in our analysis there is no need to impose the small angular momentum limit for the black hole spectroscopy.This method is simple and universal.2.Considering the influence of GUP,we first investigate the fermion's tunneling radiation and the remnant in a three dimensional G?del spacetime.It is found that,the parameters of G?del and GUP have important effects on the quantum correction to tunneling radiation and the remnant of the three-dimensional G?del black hole,and the black hole remnant may exist only when the certain condition is satisfied,which is different from the gravitational background of non-G?del spacetime.Then we discuss the quantum gravity correction to fermion tunneling and the remnant in a five-dimensional axisymmetric Myers-Perry black hole.The result shows that there exist nonlinear terms in the imaginary part of the action.This means the tunneling spectrum is no longer purely thermal,and the information may be supplied in correlations between tunneling modes.Furthermore,we find that the quantum gravity correction influenced by GUP can slow down the temperature increase,and prevents the black hole from evaporating totally,resulting in a black hole remnant.So it is also possible to maintain information conservation.Finally,we extend this method to the case of a high-dimensional G?del black hole.The results show that the quantum tunneling method influenced by GUP is still effective in this gravitational background.3.Based on the quantum tunneling influenced by GUP,we study the phase transition and the stable remnant of a Finsler black hole.The results show that the remnant of the black hole is closely related to the Planck mass,Finsler parameter and GUP parameter.We find that there is a critical mass when the mass of a Finsler black hole approaches the Planck scale.The modified heat capacity is divergent at the critical mass,which implies that the black hole with negative heat capacity undergoes a phase transition to the black hole with positive heat capacity.Furthermore,by considering the influence of quantum gravitational effect,the modified temperature of the Finsler black hole increases with the decrease of mass,and it arrives at the maximum value at the critical mass.When the mass is less than the critical mass,the revised temperature monotonically decreases with the mass decreasing.As the mass decreases to approach the minimum mass,the revised Hawking temperature and the modified heat capacity tend to be zero,and the entropy attains the minimum value.Thus,evaporation of the black hole stops,and the black hole can not change the energy with the surrounding environment.As a consequence,it forms a stable remnant in the Finsler gravity background,which avoids the appearance of the black hole's nack singularity and the black hole information loss paradox.In addition,our results show that the Finsler black holet both radiating fermions and scalar particles can form stable remnant at the final stage of evaporation.4.With motivation by holography,besides black hole entropy,we mainly use entanglement entropy,two-point correlation function and Wilson loop to survey the phase structure for a five dimensional AdS hairy black hole including the effects of the scalar field hair,and show the effect of hairy parameters on the phase transition.The results show that,in a fixed scalar charge ensemble,by selecting appropriate hairy parameters,entanglement entropy,two-point correlation function and Wilson loop can successfully capture information of the phase structure of a five-dimensional AdS hairy black hole,and exhibit the holographic Van der Waals phase transition similar to black hole entropy.At the same time,for a first order phase transition we check numerically the equal-area construction.For the second order phase transition,we obtain the same critical exponent as that of the Van der Waals phase transition in a liquid-gas system by numerical calculation.Furthermore,we extend our work to the more complex case of a charged AdS hairy black hole.The critical values of phase transition are calculated by numerical method and the phase transition curves of scalar isocharges are plotted.The results show that in canonical ensemble(with fixed electric charge),by selecting appropriate hairy parameters,using entanglement entropy and two-point correlation function,we can observe the holographic Van der Waals phase transition like the black hole entropy.In addition,for the entanglement entropy and two-point correlation function,we perform a large number of numerical computations to equal-area law with different charge ratios.As a result,we find that Maxwell equal area law is only valid near the critical point.Away from the critical point,the relative error becomes significantly large,and the Maxwell equal-area law cannot hold.