标题： 可能的流体解释和爱因斯坦-卡坦理论中一般类光超曲面上的潮汐力方程 显示英文标题

标题： Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory

摘要： Hajicek$1$形式的动力学演化是在爱因斯坦-卡坦(EC)理论中推导出来的。 我们发现，类似于爱因斯坦引力理论，演化方程与在一般 null 表面$\mathcal{H}$上的爱因斯坦张量$(\hat{G}_{ab})$的投影部分有关，特别是$\hat{G}_{ab}l^a q^b_{~c}$，其中$l^a$和$q^a_{~c}$是$\mathcal{H}$的向外 null 生成元，以及$\mathcal{H}$的横向空间截面的诱导度规。 在{\it 测地线约束}下，提出了该演化方程的可能流体解释。 我们发现，如果我们用与$\mathcal{H}$相适应的坐标系以及局部惯性系来表达 Hajicek$1$-形式的动力学演化方程，其结构就类似于 Navier-Stokes 流体的{\it 科舍尔特广义}。 从认为流体的通常物质导数应被李导数取代的观点出发，也可以建立类似的观点。 最后，也推导了 EC 理论中在零面上的潮汐力方程。 显示英文摘要

摘要： 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.