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We study the invariant Planck scale correction to the thermodynamics of theideal Fermi gas. We have considered the modified dispersion relation and thecut-off to the maximum possible momentum/energy (Planck energy) of thenon-interacting ideal degenerate Fermi gas particles. With such a modificationthe expression for the degenerate pressure and the total energy gets modifiedaccordingly. We discuss the number density and mass dependence of thedegenerate pressure. We found that the degenerate pressure is perturbative inthe SR limit. We then take the example of white dwarfs to explore the possibleimplications. Using this modified degenerate pressure, we calculate thepossible modification to the Chandrashekhar limit for white dwarfs using theMagueijo-Smolin (MS) modified dispersion relation. The mass-radius M-R plotshows that the modified/corrected radius of the white dwarf can be greaterthan, equal to and smaller than the usual special relativity (SR) value forparticular masses. We found that the Chandrasekhar mass limit gets a positivecorrection. We note that the presence of observed white dwarfs having radiussmaller than the SR Chandrasekhar limit may find an explanation if they aremodeled using a modified dispersion relation. As the correction is perturbativein the SR limit, therefore this correction is solely because of the modifieddispersion relation. The value of the obtained degenerate pressure for a givenmass is found to be greater than, equal to and smaller than the usual specialrelativity (SR) value for particular masses as expected. We have alsocalculated the luminosity of the white dwarf by taking the model of partiallydegenerate gas and considering the modified radiative envelope equation. Theluminosity also gets a negative correction. The correction to luminosity isnonperturbative as expected for such a theory.

Invariant ultraviolet scale corrections to the thermodynamics of degenerate Fermi gas and its implications