Nouri-Zonoz M, Nourizonoz A
Department of Physics, University of Tehran, North Karegar Ave., Tehran, 14395-547, Iran.
Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran, 19839, Iran.
Sci Rep. 2022 Sep 2;12(1):15032. doi: 10.1038/s41598-022-18979-y.
The usual characterization of exact solutions of Einstein field equations, including cosmological solutions, is based on the symmetry properties of their corresponding metrics which is obviously mathematically involved. Here we present a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations by employing the [Formula: see text] formulation of spacetime decomposition which introduces the so-called quasi-Maxwell form of the Einstein field equations in the broader context of gravitoelectromagnetism. These solutions have a single or 2-component perfect fluid sources, and are characterized according to their gravitoelectric and gravitomagnetic fields which are the gravitational analogs of the electromagnetic fields. It is shown that the absence or presence of either or both of these fields could restrict the equations of state of the contributing perfect fluid sources. As the representative of each family of solutions, we consider those spaces that include the cosmological term as a dark fluid source with the equation of state [Formula: see text].
爱因斯坦场方程精确解（包括宇宙学解）的通常特征描述是基于其相应度规的对称性，这显然涉及数学内容。在此，我们通过采用时空分解的[公式：见原文]形式，给出爱因斯坦场方程静态和稳态理想流体解的一种物理特征描述，该形式在广义引力电磁学背景下引入了所谓的爱因斯坦场方程的准麦克斯韦形式。这些解具有单组分或双组分理想流体源，并根据它们的引力电场和引力磁场来表征，引力电场和引力磁场是电磁场的引力类似物。结果表明，这些场中任意一个或两个的存在与否都可能限制贡献理想流体源的状态方程。作为每个解族的代表，我们考虑那些将宇宙学项作为具有状态方程[公式：见原文]的暗流体源的空间。
