International Journal of Geometric Methods in Modern Physics ( IF 1.8 ) Pub Date : 2022-07-06 , DOI: 10.1142/s0219887822501717 Wladimir-Georges Boskoff 1
The problem of FLRW universes can be seen in the excellent works of A. Friedmann, G. Lemaître, H. P. Robertson, A. G. Walker. The key of obtaining FLRW universes with or without cosmological constant is related to the special form of the contravariant energy–momentum tensor which describes a perfect fluid with components
The answer is yes and we prove the special role of the constant ratio in the creation of FLRW universes. The solutions obtained lead to FLRW universes which come from surfaces having constant Gaussian curvature related by the previous from the rule . Therefore, in the case of the 2D metrics , only the ones having constant Gaussian curvature create FLRW universes. In fact, we find all possible FLWR-type solutions of Einstein field equations coming from constant Gaussian curvature geometries. We complete our study about possible FLRW universes with an example of a spacetime that cannot be “filled” with matter using the above FLRW conditions. This becomes a new example of universe without matter satisfying the Einstein’s field equation with cosmological constant.
中文翻译:
恒定高斯曲率、FLRW 条件和无物质宇宙
FLRW 宇宙的问题可以在 A. Friedmann、G. Lemaître、HP Robertson、AG Walker 的优秀作品中看到。获得有或没有宇宙学常数的 FLRW 宇宙的关键与描述具有分量的完美流体的逆变能量-动量张量的特殊形式有关
答案是肯定的,我们证明了恒比的特殊作用在创造 FLRW 宇宙中。获得的解决方案导致 FLRW 宇宙来自具有与前面相关的恒定高斯曲率的表面从规则. 因此,在二维度量的情况下,只有具有恒定高斯曲率的那些才能创建 FLRW 宇宙。事实上,我们发现爱因斯坦场方程的所有可能的 FLWR 型解都来自恒定高斯曲率几何。我们通过使用上述 FLRW 条件无法“充满”物质的时空示例来完成对可能 FLRW 宇宙的研究。这成为没有物质满足爱因斯坦场方程的宇宙学常数的新例子。