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.

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• Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
• Gravitational instability of isothermal and polytropic spheres
• Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
• Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars
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• Gravitational instability of polytropic spheres and generalized thermodynamics
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• 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

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• Ion-Acoustic Envelope Modes in a Degenerate Relativistic Electron-Ion Plasma
• Instability of a uniformly collapsing cloud of classical and quantum self-gravitating Brownian particles
• Bonnor stars in d spacetime dimensions
• Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
• Critical dynamics of self-gravitating Langevin particles and bacterial populations
• Statistics of the gravitational force in various dimensions of space: from Gaussian to Levy laws
• Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
• Gravitational phase transitions with an exclusion constraint in position space
• Extra dimensions' influence on the equilibrium and radial stability of strange quark stars
• Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars
• Planck scale effect on the thermodynamics of photon gas
• Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: evolution of density profiles with temperature
• A No-Go Theorem for the Mass-Radius Relation of Solitons