The Idea Bose Gas In Static Space Time

In this paper,the general relativity method is used to study the small box ideal Bose gas in static space-time and the two-dimensional spherical Bose gas surrounding the black hole horizon.The density of states and the macro partition function as well as the statistical expressions of the thermodynamic quantities(including the average energy E and the average number of particles N as well as the average entropy S and the average pressure P)of the two models are obtained.The results show that these partition functions and statistical expressions of thermodynamic quantities are affected by the gravitational field,especially near the horizon of the black hole these physical quantities will exhibit a divergent behavior.When the Bose gas system is far away from the source of the gravitational field,these Partition functions and statistical expressions of thermodynamic quantities can return to the case of non-relativity or extreme relativity.In addition,the critical temperature Tc for the Bose-Einstein condensation(BEC)and the condensation ratio N0/N of the two models were also studied.The results show that the critical temperature will be affected by the gravitational field,especially near the horizon of the black hole,the critical temperature will tend to zero;when the Bose gas is far from the source of gravity,the critical temperature will return to the cases of non-relativity or extreme relativity.However,the formula of the condensation ratio is still the same as the case of non-relativity and extreme-relativity.In addition,through the Lorentz transformation of the state variable,the Lorentz transformation properties of Maxwell relationship andthe three laws of thermodynamics of the thermodynamic system in the flat spacetime are also studied.The results show that within the framework of the Planck transformation,the Maxwell relationship of thermodynamics and the three laws of thermodynamics have Lorentz invariance,that is,the Maxwell relationship and the three laws of thermodynamics have nothing to do with the reference system.At the same time,this paper also proves that the expressions "the mass object cannot reach the speed of vacuum light" and "the temperature of the object cannot reach absolute zero" under the framework of the Planck temperature transformation are equivalent.It laid a foundation for further study of the covariance of the thermodynamic system of bending space-time.