标题： 白矮星在D维空间中 显示英文标题

标题： White dwarf stars in D dimensions

摘要： 我们确定了相对论白矮星（温度为0的自引力简并费米气体）在D维宇宙中的质量-半径关系，并研究当结合量子力学、狭义相对论和引力时，空间维度对物理定律的影响。 我们展示了特征维度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，即使在非相对论情形下，量子力学也无法平衡引力坍缩。 这类似于Ehrenfest（1917）在原子层面发现的结果，针对库仑力（在Bohr模型中）和开普勒问题。 这使得我们宇宙的维度D=3非常特殊。 我们讨论了与Chandrasekhar（1931b）极限质量发现相关的历史方面，以及与Anderson（1929）和Stoner（1930）之前的研究之间的关系。 我们还展示了白矮星的Chandrasekhar极限质量与二维趋化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.