论文标题
一般相对论中的d维自生长晶格气体
D-dimensional self-gravitating lattice gas in general relativity
论文作者
论文摘要
使用状态的晶格方程与D维tolman-Oppenheimer-volkoff方程和弗里德曼方程相结合，我们研究了紧凑对象形成的可能性以及比例因子的时间演变以及自gravitating材料群集的密度分布的时间演变。数值结果表明，在$ 2+1 $尺寸的时空中，质量与中心压力无关。因此，只有有限常数质量与白矮人相似的紧凑型物体的形成是可能的。但是，在$ 3+1 $尺寸的时空中，自我实现会导致形成具有较大质量间隙的紧凑物体，相应的相图具有与中子星的结构相同的结构。结果还表明，在某些临界中心压力之外，恒星对重力塌陷不稳定，并且可能以黑洞结束。对较高维度的间距的分析表明，重力在$ 3+1 $尺寸中具有更强的效果。 Friedmann方程的数值解决方案表明，时空曲率的效果随温度的升高而增加，但随着尺寸的增加而下降，超过$ d = 3 $。
Using a lattice equation of state combined with the D-dimensional Tolman-Oppenheimer-Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a $2+1$ dimensional spacetime, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a $3+1$ dimensional spacetime, self-gravity leads to the formation of compact objects with a large gap of mass and the corresponding phase diagram has the same structure as the one for Neutron Star. The results also show that beyond certain critical central pressure, the star is unstable against gravitational collapse, and it may end in a black hole. Analysis of spacetimes of higher dimensions shows that gravity has the stronger effect in $3+1$ dimensions. Numerical solutions of the Friedmann equations show that the effect of the curvature of spacetime increases with increasing temperature, but decreases with increasing dimensionality beyond $D=3$.
