Research On Curved Space-time And Quantum-gravity Theory

The research on the related problems of curved space-time and quantum gravity theory is one of the hot and frontier topics in theoretical physics and astrophysics.In order to further reveal the nature of gravity and space-time,we use the results of ultra-precise experiment to constrain the forms of the deformed energy-momentum dispersion relation with Planck-scale sensitivity in the non-relativistic limit,study the effect of double special relativity(DSR)and Lorentz invariance breaking on Hawking radiation of black holes,construct a new generalized uncertainty principle(GUP)with higher-order correction terms,and study the effect of the new GUP on the thermodynamic properties of black hole evaporation.In this dissertation,it not only combines theoretical research with experimental observation,but also carries out theoretical development and application research.It belongs to the interdisciplinary study of theoretical physics and dense astrophysics,and is also the application study of the effective theory of quantum gravity.The contents are divided into five parts shown as follows.1.We use the latest results of the ultra-high accuracy 1S-2S transition experiments in the hydrogen atom to constrain the forms of the deformed dispersion relation with Planck-scale sensitivity.For the leading correction of the non-relativistic limit,the experiments set a meaningful limit at an order of magnitude for the desired Planck-scale level,i.e.|?1|?1.3,which is the same as that of the cold atom recoil experiments ?1=-1.8±2.1.This means that the ultra-high accuracy 1S-2S transition experiments can be used to study the quantum properties of gravity at the desired Planck-scale sensitivity,thereby providing another example in the study of the dispersion relation in controlled laboratory experiments.For the next-to-leading term,this result allows us to establish bound |?2|<1.7 × 102,which is two orders of magnitude away from the Planck-scale,however it still amounts to the best bound in thenon-relativistic limit,in contrast to the previously obtained bound |?2|<109 from the cold-atom-recoil experiments.2.Based on the deformed dispersion relation in DSR,the effect of the Planck-scale on the Hawking radiation is extended from the space-time of the static and stable black holes to that of the dynamic black holes.Starting from the Rarita-Schwinger equation,which describes the motion equation of the more general fermions,the semi-classical approximation method is applied to obtain the modified Hamilton-Jacobi equation with the Planck-scale effect,which is compared with the previous study on the motion equation of the fermions with the spin of 1/2.Then,the fermions' tunneling radiation from the non-stationary symmetric Kerr black hole is studied by using the modified Hamilton-Jacobi equation.The results show that the Planck-scale effect modify the thermodynamics properties of the black hole,and for the non-stationary symmetric Kerr black hole,the modified Hawking temperature and the modified tunneling rate at the horizon are not only the radial properties of the black hole,but also the angular properties of the black hole3.Banerjee-Ghosh's work shows that the singularity problem can be naturally avoided by the fact that the black hole evaporation stops at the remnant mass greater than the critical mass when including the GUP effects with the first-order and second-order corrections.In this dissertation,we follow their steps to reexamine the Banerjee-Ghosh's work,but find an interesting result that the remnant mass is always equal to the critical mass at the final stage of the black hole evaporation with the inclusion of the GUP effects.In addition,we can easily find that the thermodynamic quantities are not singular at the final stage of the black hole evaporation with the inclusion of quantum gravity effect.In fact,the critical mass is derived from the third law of thermodynamics about the effective range of temperature,and the remnant mass is derived from the fact that the heat capacity is equal to zero or the entropy of the black hole does not change with its mass.The equality between the remnant mass and the critical mass means that the corresponding relationship between the third law of thermodynamics and the cosmic censorship hypothesis established in classical gravity is still valid in quantum gravity.This reveals that the third law of thermodynamics can be used as the supervisor of the causality that quantum space-time cannot exceed the Planck scale,which may provide a thermodynamic origin for explaining the existence of a minimum observable length in quantum gravity4.Based on the idea of S.Hossenfelder et al.to construct the GUP relation,a new GUP with higher-order correction terms is constructed by modifying the de Broglie relation.Compared with the Banerjee-Ghosh's GUP established from three basic assumptions,the new GUP gives a specific function form between the wave vector and the momentum of particles.Subsequently,we use the new GUP to study the evolution behavior of Schwarzschild black hole at the final stage of evaporation.It is found that the black hole does not completely evaporate when considering the quantum gravity effects,and the black hole evaporation always stops at the remnant mass equal to the critical mass.The result confirms once more that the corresponding relationship between the third law of thermodynamics and the cosmic censorship hypothesis still holds in quantum gravity.Finally,by analyzing the behavior of the black hole remnant based on the new GUP relation,it is found that the type of the black hole remnant is closely dependent on the positive or negative correction terms in the GUP relation.5.Based on the standard model extension(SME)theory,a new method is proposed to study the effects of the Lorentz invariance breaking on the Hawking radiation of black holes.By associating the Lorentz invariance breaking with the tunneling radiation characteristics,it can help us to understand the quantum effect of Lorentz invariance breaking more deeply.In this dissertation,we study the effects of the Lorentz invariance breaking on the radiation characteristics of the scalar particles and fermions via Hawking radiation from the charged Reissner-Nordstrom and dynamic Vaidya black hole.The results show that the Lorentz invariance breaking terms modify the tunneling radiation properties of the black holes,especially for the spinor field,only the aether-like Lorentz-breaking term affects the tunneling radiation characteristics of fermions,which is independent of the CFJ and the chiral Lorentz-breaking terms.