High-order Corrections To Thermodynamic Quantities Of Bose Systems In Curved Spacetim

The thermodynamic study of a black hole has attracted a great deal of attention since Hawking demonstrated Hawking radiation using quantum field theory in curved spacetime.This dissertation begins with a brief review of the formation and definition of a black hole,and gives a rigorous mathematical definition and a local definition that is easy to use in physics.This dissertation then presents different computational models that have been proposed to explain the statistical origin of black hole entropy in various theoretical frameworks.One of these that has been widely discussed is ’t Hooft’s brick wall model.With further study of the brick wall model,researchers have found that it has two main drawbacks: one is that it assumes thermal equilibrium;the other is that it takes a small mass approximation.To address these two problems,the thin layer model was proposed.Related research in string theory proposed a Generalised Uncertainty Principle(GUP),which is an extension of Heisenberg’s uncertainty principle in curved spacetime.It is worth mentioning that after this conclusion was obtained in the framework of string theory,measurements on black holes from the level of the Gedanken experiment also led to a model-independent conclusion similar to the GUP.This suggests that classical physical laws may need to be modified after taking into account quantum effects and spacetime curvature effects.The first work of this dissertation is to investigate the Bose system outside a Schwarzschild black hole using the thin layer model.The Klein-Gordon equation in curved spacetime is used to solve the energy-momentum relation for the boson.Secondly,the generalised uncertainty principle is introduced in the phase space,and the Bose statistical method is adopted to calculate the grand partition function and the associated statistical expressions of thermodynamic quantities.The results show that the expressions in curved spacetime are different from the flat spacetime.They have a higher order correction term due to the generalised uncertainty priciple,and that their coefficients are related to the background spacetime.Moreover,we also calculated these thermodynamic quantities under extreme physical condition.The second work of the dissertation discusses the Fermi degeneracy pressure in curved spacetime.Different from Hawking radiation,we treat fermion as a particle and use four momentum contraction to obtain its energy-momentum relation.Under absolute zero condition,the distribution of fermions is used to calculate the total number of particles and the corresponding Fermi degeneracy pressure.