We study the invariant Planck scale correction to the thermodynamics of the ideal Fermi gas. We have considered the modified dispersion relation and the cut-off to the maximum possible momentum/energy (Planck energy) of the non-interacting ideal degenerate Fermi gas particles. With such a modification the expression for the degenerate pressure and the total energy gets modified accordingly. We discuss the number density and mass dependence of the degenerate pressure. We found that the degenerate pressure is perturbative in the SR limit. We then take the example of white dwarfs to explore the possible implications. Using this modified degenerate pressure, we calculate the possible modification to the Chandrashekhar limit for white dwarfs using the Magueijo-Smolin (MS) modified dispersion relation. The mass-radius M-R plot shows that the modified/corrected radius of the white dwarf can be greater than, equal to and smaller than the usual special relativity (SR) value for particular masses. We found that the Chandrasekhar mass limit gets a positive correction. We note that the presence of observed white dwarfs having radius smaller than the SR Chandrasekhar limit may find an explanation if they are modeled using a modified dispersion relation. As the correction is perturbative in the SR limit, therefore this correction is solely because of the modified dispersion relation. The value of the obtained degenerate pressure for a given mass is found to be greater than, equal to and smaller than the usual special relativity (SR) value for particular masses as expected. We have also calculated the luminosity of the white dwarf by taking the model of partially degenerate gas and considering the modified radiative envelope equation. The luminosity also gets a negative correction. The correction to luminosity is nonperturbative as expected for such a theory.
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