Correction Of Tunneling Radiation And Entropy Of Black Hole By GUP

In this paper,Quantum Corrected Schwarzschild black hole,Kehagias-Sfetsos black hole and Rutz-Schwarzschild black hole are taken as examples to study the correction of black hole Hawking radiation and entropy by Generalized Uncertainty Principle(GUP).Different GUP forms are used to correct the tunneling radiation of scalar particles and vector particles,and the tunneling rate,Hawking temperature and heat capacity based on GUP correction are calculated.It is found that they are not only constrained by the black hole mass and space-time background,but also affected by the GUP parameters,so the Hawking radiation spectrum obtained in this paper is not pure heat.From the images of temperature-mass(T-M)and heat capacity-mass(C-M)of the black hole,it can be seen that after considering the influence of GUP,the corrected Hawking temperature is lower than the classical Hawking temperature,and the corrected heat capacity is lower than the traditional heat capacity,the classic curve and the correction curve tend to be consistent over a large mass range.But when the black hole evaporates to a critical mass on the Planck scale,the corrected heat capacity is abruptly changed from negative infinity to positive infinity,which means that the phase transition occurs.As the black hole evaporates to the minimum mass,the corrected Hawking temperature and heat capacity tend to zero,and the black hole stops the energy exchange with the external environment,therefore a stable remnant is produced in the final stage of thermodynamic evolution.The above results show that GUP has a great influence on the tunneling process of black holes,that is,GUP can escape the black hole from evaporating completely,resulting in the black hole stopping radiating at the remnant.The corrected black hole entropy is obtained based on the first law of thermodynamics and the corrected Hawking temperature.In addition to the mass of the black hole and the space-time background,the modified entropy is also affected by the type of radiating particles and the GUP parameters.Its expression is more complex than the classical entropy form,including corrections such as fractional andlogarithmic,which provide more possibilities for the interpretation of the microscopic origin of black hole entropy.By observing the entropy-mass(S-M)image,it is found that when the black hole is close to the Planck scale,there is a significant difference between the modified curve and the classical curve.And when the black hole evaporates to the minimum mass,the modified entropy reaches the minimum value,that is,there exists the residual entropy of the black hole under the influence of GUP.In summary,based on GUP study of tunneling radiation and entropy correction of black holes,we can draw a lot of results which is worthy of in-depth analysis and thinking.Under the correction of GUP,there are many corrections for the thermodynamic quantity of the classical black hole with simple form.The black hole that completely evaporated at the remnant.stops evaporation.The original black hole entropy is approximately zero,and the residual entropy appears after correction.It means that the information of the black hole evaporation to the final stage has not completely disappeared,which provides a reference value for solving the problem of black hole information loss.