Research On Black Hole Thermodynamics Under The Generalized Uncertainty Principl

In the early days of black hole thermodynamics,Bekenstein and Hawking first combined general relativity with thermodynamics and used it to explore the thermodynamic properties of black holes.On the basis of Hawking’s black hole area theorem,Bekenstein proved the existence of entropy as a thermodynamic property of black holes.Taking the semi-classical quantum field theory as a benchmark,Hawking then pointed out that black holes not only absorb matter but also emit thermal radiation,which is the famous Hawking radiation.Hawking radiation theory effectively proved the concept of the existence of temperature of black holes,and the four laws of black hole thermodynamics were established in turn,which laid the foundation for the study of black hole thermodynamics.However,since there are still some problems with the semiclassical quantum tunneling radiation,we need to introduce the generalized uncertainty principle(GUP)into the classical Hawking radiation theory and discuss the correction of GUP to black hole thermodynamics.In this paper,we investigate the thermodynamic properties of Schwarzschild black holes and Reissner-Nordstr(?)m(RN)black holes using the linear extended generalized uncertainty principle(LEGUP),and we investigate the Banados-Teitelboim-Zanelli(BTZ)black hole using the new extended uncertainty principle(NEUP).thermodynamics.First,the minimum temperature and the modified mass temperature function of the Schwarzschild black hole are calculated by establishing the theoretical framework of LEGUP.Further,the heat capacity function of the Schwarzschild black hole is obtained.Then,we also discuss the correction of the black hole entropy,which is applied to the heuristic analysis of the particles absorbed by the black hole.In addition,the thermodynamic properties of LEGUP black holes are compared with those of EGUP black holes,as well as those of black holes in their usual form.After that,we also derive the temperature function,heat capacity function and entropy function of the RN black hole modified by LEGUP.Finally,we investigate the temperature,entropy,thermodynamic volume,Gibbs free energy,pressure and heat capacity of the BTZ black hole at(A)d S spacetime using NEUP.And we analyze these thermodynamic quantities on Ad S spacetime and d S spacetime,taking different parameter values for comparison,and elaborate the corrections of the thermodynamic properties of the BTZ black hole under NEUP respectively.