Influence Of Thermal Fluctuation And GUP On Black Hole Thermodynamics

Since Bekenstein proposed the concept of black hole area entropy and Hawking discovered Hawking radiation,black hole thermodynamics has become a hot research field.Researchers have done a lot of work from the geometric and thermodynamic properties of black holes,trying to reveal the nature of black holes and the statistical origin of black hole entropy.In this thesis,we study the effects of thermal fluctuation and generalized uncertainty principle(GUP)on the entropy and thermodynamic properties of black holes.In this thesis,we use the canonical ensemble partition function,and assume that the black hole's Bekenstein-Hawking entropy as a function of temperature has an extreme point under the condition of considering the thermal fluctuation.After a series of mathematical transformation,the modified expression of entropy of black hole caused by thermal fluctuation is obtained,that shows the same conclusion as other methods,i.e.the first term of the modified entropy expression is the classical Bekenstein-Hawking entropy,the second term is the logarithm of the BekensteinHawking entropy,and the third term is the reciprocal of the classical black hole entropy.According to this modified relation,we study the influence of thermal fluctuation on the thermodynamic properties of non-rotating BTZ black hole and charged GMGHS dilaton black hole.For the non-rotating BTZ black hole,considering entropy as a function of event horizon,we find that there is a critical value for the effect of thermal fluctuation on the entropy of this black hole.Before this critical value,thermal fluctuation will increase the entropy of the black hole,when the even horizon radius of the black hole is greater than this critical value,thermal fluctuation will reduce the entropy of the black hole.By studying the heat capacity of the non-rotating BTZ black hole,we find that this black hole is a stable system without considering the thermal fluctuation correction.When considering thermal fluctuation corrections,the non-rotating BTZ black hole with small event radius will become unstable,while the thermal fluctuation will not change the stability of the large black hole.For the charged GMGHS dilaton black hole,the entropy of the black hole will increase after considering the thermal fluctuation.By studying the influence of thermal fluctuation on the heat capacity of this black hole,we find that the GMGHS black hole itself is an unstable system.For the smaller GMGHS black hole,the thermal fluctuation will make the black hole become stable,for the larger GMGHS black hole,thermal fluctuation will not change their stability,which is consistent with the non rotating BTZ black hole.In the third chapter,we calculate the entropy of the general static black hole by using the quantum state number of the phase space modified by the generalized uncertainty principle.It is found that the result is consistent with the conclusion obtained by other methods,that is,the entropy of the black hole is proportional to its event horizon area,but we do not introduce the cutoff artificially in the calculation process,and we do not consider the small mass approximation.At the same time,according to the entropy function modified by the generalized uncertainty principle,we study the influence of the generalized uncertainty principle on the thermodynamics of the Bardeen-Ad S black hole.We find that the Hawking temperature and thermodynamic pressure of the black hole increase with the modification of the generalized uncertainty principle.At the same time,the modification of the generalized uncertainty principle brings an additional phase transition phenomenon to the black hole.Under the modified generalized uncertainty principle,there will be a Planck scale remnant in the evolution of the black hole.