Thermodynamics And Weak Cosmic Censorship Conjecture Of Higher Dimensional F(R) Black Holes In The Different Phase Space

The black hole,as the most mysterious celestial body in the universe,has been the subject of intense discussion.The study of black holes has also been an interesting and meaningful subject in modern theoretical physics.Among them,the study of black hole thermodynamics is particularly important,the black hole not only has many interesting similarities as thermodynamic systems and general thermodynamic systems,but the study of black hole thermodynamics makes the three fields of general relativity,thermodynamics and quantum mechanics possible closely connected.In the research process based on the temperature,entropy and laws of thermodynamics of black holes,when the cosmological constant is regarded as a dynamic variable(defining the cosmological constant as the pressure of the black hole,and its thermodynamic conjugate variable is the volume).As a result,the thermodynamic phase space was expanded,and the laws of thermodynamics were re-established in the expanded phase space,and a richer phase structure of the black hole was also discovered.In this framework,some studies have also made great progress,including P-V critical,Joule-Thomson expansion,black hole heat engine efficiency,and so on.In this paper,with the Hamilton-Jacobi equation and Dirac equation,we obtain the energy-momentum relation of a charged particle(charged scalar particle or fermion)as it is absorbed by the higher dimensional f(R)black hole.On the basis of the energymomentum relation at the event horizon,we investigate the first law,second law,and weak cosmic censorship conjecture in the different phase space.In the normal phase space,the cosmological constant is set to a constant value,and we find that the laws of thermodynamics as well as the weak cosmic censorship conjecture are valid.Additionally,our results show the final configuration of the black hole does not change,when the extremal f(R)black hole absorbed the charged particle.In other words,the extremal higher-dimensional f(R)black holes still an extremal black hole in the course of the absorption.In the extended phase space,the cosmological parameter is identified as a variable which is interpreted as a pressure.We find that though the first law of thermodynamics still valid,the entropy of the extremal or near-extremal black hole is decrease during the irreversible process of black holes swallow the charged particle,in this case,the second law is invalid.Interestingly,we also find that the near-extremal higher-dimensional f(R)black hole(excluding four-dimensional cases)could be overcharged in the course of the absorption,that is,the horizon of the black hole will disappear.In other words,the weak cosmic censorship conjecture may be invalid when the charged particle dropped into the higher-dimensional near-extremal f(R)black holes,and the magnitudes of the violation is related to those of the parameters.