Research On Black Hole Phase Transition With Generalized Uncertainty Principle

This article explores the tunneling radiation of scalar particles under the generalized Hamilton-Jacobi(H-J)equation and fermions under the generalized Dirac equation and quantum-corrected black hole phase transitions.Taking asymptotic safety(AS)improved Schwarzschild black hole and Rindler modified Schwarzschild black hole as examples,the temperature and heat capacity are discussed separately,and the thermodynamic behavior is analyzed.Then we analyze the phase transition and thermodynamic properties of Rutz-Schwarzschild(RS)black hole in Finsler geometric framework.Based on the generalized uncertainty Principle(GUP),the scalar particles and fermions emitted by the modified Schwarzschild black hole continuously evaporate,and the mass and temperature of the black hole will change.The modified Hawking temperature is similar to the standard Hawking temperature in a large mass range,and both increase with decreasing mass,but when the black hole evaporates to Planck mass,there is a significant difference between the two.The corrected Hawking temperature no longer rises at the critical massM(28)M_c,but drops rapidly and eventually produces residual material.The heat capacity suddenly cuts off atM(28)M_c and changes from negative to positive.As the black hole continues to evaporate,the final heat capacity value is zero,resulting in residual matter,indicating that the black hole did undergo a thermodynamic phase transition.At the end of the article,the phase transition and thermodynamic properties of RS black hole under the Finsler geometry framework are studied.Based on GUP,the modified thermodynamic quantities such as tunneling temperature,local temperature,heat capacity,and black hole entropy are calculated.Through these corrections,the phase transition and thermodynamic behavior of RS black holes are analyzed.We have many different findings compared to the thermodynamic quantities of the original Schwarzshild black hole.First,the GUP prevents black holes from completely evaporating and produces a stable remnant.Second,the range of the generalized uncertainty parameter will affect the phase transition of the black hole.In addition,we also found that stable small black holes(SBH)and stable large black holes(LBH)can exist for a long time with increasing temperature.In short,using the GUP to discuss the thermodynamic phase transition of a black hole,we can obtain many results worth deep analysis.Under the correction of the GUP,a correction term appears in the classic black hole thermodynamic quantity in a simple form.The black hole no longer completely evaporates and eventually produces a residue.This indicates that the thermodynamic evolution of the black hole has reached the final stage and the informations have been saved.