White dwarf stars in D dimensions

Abstract

We determine the mass-radius relation of relativistic white dwarf stars (a self-gravitating degenerate Fermi gas at T=0) in a D-dimensional universe and study the influence of the dimension of space on the laws of physics when we combine quantum mechanics, special relativity and gravity. We exhibit characteristic dimensions D=1, D=2, D=3, D={1\over 2}(3+\sqrt{17}), D=4, D=2(1+\sqrt{2}) and show that quantum mechanics cannot balance gravitational collapse for D\ge 4, even in the non-relativistic regime. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulomb forces (in Bohr's model) and for the Kepler problem. This makes the dimension of our universe D=3 very particular. We discuss some historic aspects concerning the discovery of the Chandrasekhar (1931b) limiting mass in relation with previous investigations by Anderson (1929) and Stoner (1930). We also show the analogy between the Chandrasekhar limiting mass of white dwarf stars and the critical mass of biological populations in the two-dimensional chemotactic problem.

References in corpus (3)

• Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions
• Dynamical stability of collisionless stellar systems and barotropic stars: the nonlinear Antonov first law
• Newtonian gravity in d dimensions

Cited by in corpus (4)

• Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes
• Bonnor stars in d spacetime dimensions
• Critical dynamics of self-gravitating Langevin particles and bacterial populations
• Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars