Modified structure equations and mass–radius relations of white dwarfs arising from the linear generalized uncertainty principle

Abstract

The generalized uncertainty principle (GUP) is a common feature among several approaches related to quantum gravity. An approach to GUP was recently developed that contains both linear and quadratic terms of momenta, from which an infinitesimal phase space volume was derived up to the linear term of momenta. We studied the effects of this linear GUP approach on the structure equations and mass–radius relation of zero-temperature white dwarfs. We formulated a linear GUP-modified Chandrasekhar equation of state (EoS) by deriving exact forms of the thermodynamic properties of ideal Fermi gases. This was then used to obtain the analytical form of the modified Newtonian structure equations for the white dwarfs. By imposing a constraint on the momenta of the particles in the white dwarf due to linear GUP, the structure equations were solved and the modified mass–radius relation of the white dwarfs were obtained. This was then extended in the context of general relativity (GR), which, like linear GUP, affects white dwarfs significantly in the high-mass regime. We found that linear GUP displays a similar overall effect as in GR — linear GUP supports gravitational collapse of the white dwarf, by decreasing its limiting (maximum) mass and increasing its corresponding limiting (minimum radius). We also found that GUP effects become evident only at large values of the GUP parameter, but these values are still within the estimated bounds. This effect gets more prominent as we increase the as-of-yet unestablished value of the parameter.