论文标题
在爱因斯坦 - 卡丹理论中，可能的流体解释和潮汐力方程
Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory
论文作者
论文摘要
哈吉斯克$ 1 $形式的动态演化是在爱因斯坦 - 卡丹（EC）理论中得出的。我们发现，像爱因斯坦的重力理论一样，演变方程与Einstein张量的投影部分有关（\ hat {g} _ {ab}）$上的通用零表面$ \ mathcal {h} $，尤其是$ \ hat {g} _ {ab} _ {ab} l^a q^a q^a q^a q^a q^a q^a q^a q^a q^a q^ab} $ q^a_ {〜c} $是$ \ mathcal {h} $的null发电机，分别为$ \ Mathcal {H} $的横向空间横截面。然后，提出了对该演化方程的可能的流体解释，然后提出了{\ it Geodesic约束}。我们发现，它具有让人联想到Navier-Stokes流体的{\ it cosserat概括}的结构，前提是我们在适应于$ \ \ \ \ \ \ Mathcal {H} $的坐标中表达了Hajicek $ 1 $ form的动态演化方程。还可以在动机下建立一个类似的观点，即应用谎言衍生物代替通常的液体衍生物。最后，还得出了EC理论中的潮汐力方程。
The dynamical evolution of the Hajicek $1$-form is derived in Einstein-Cartan (EC) theory. We find that like Einstein theory of gravity, the evolution equation is related to a projected part of the Einstein tensor $(\hat{G}_{ab})$ on a generic null surface $\mathcal{H}$, particularly $\hat{G}_{ab}l^a q^b_{~c}$, where $l^a$ and $q^a_{~c}$ are the outgoing null generators of $\mathcal{H}$ and the induced metric to a transverse spatial cross-section of $\mathcal{H}$ respectively. Under the {\it geodesic constraint} a possible fluid interpretation of this evolution equation is then proposed. We find that it has the structure which is reminiscent to the {\it Cosserat generalization} of the Navier-Stokes fluid provided we express the dynamical evolution equation of the Hajicek $1$-form in a set of coordinates adapted to $\mathcal{H}$ and in a local inertial frame. An analogous viewpoint can also be built under the motive that the usual material derivative for fluids should be replaced by the Lie derivative. Finally, the tidal force equation in EC theory on the null surface is also derived.
