Mass radius scaling near the Chandrasekhar Limit

The mass radius relationship of white dwarfs, near the Chandrasekhar Limit, is derived for a toy model of uniform density, using the variational principle. A power law scaling, reminiscent of those found in 2nd order phase transitions, is obtained. The derived exponent is shown to explain the relationship obtained by numerically integrating the TOV equations with the equation of state for a relativistic Fermi gas of electrons.