标题： D维白矮星 显示英文标题

标题： White dwarf stars in D dimensions

摘要： 我们确定了D维宇宙中相对论白矮星（一个自引力的零温简并费米气体）的质量-半径关系，并研究了当结合量子力学、狭义相对论和引力时，空间维度对物理定律的影响。 我们展示出特征维度D=1、D=2、D=3、D={1\over 2}(3+\sqrt{17})、D=4、D=2(1+\sqrt{2})，并表明对于D\ge 4，即使在非相对论情况下，量子力学也无法阻止引力坍缩。 这与Ehrenfest（1917年）在原子尺度上对于库仑力（在玻尔模型中）和开普勒问题的结果类似。 这使得我们的宇宙维度D=3显得非常特殊。 我们讨论了钱德拉塞卡（1931b年）极限质量的发现与Anderson（1929年）和Stoner（1930年）先前研究之间的历史关联。 我们还展示了白矮星钱德拉塞卡极限质量和二维趋化性问题中生物种群临界质量之间的类比。 显示英文摘要

摘要： 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.