标题： 引力场的代数分类在一般度规仿射几何中 显示英文标题

标题： Algebraic classification of the gravitational field in general metric-affine geometries

摘要： 我们提出了四维一般度规仿射几何中引力场的代数分类，从而通过无迹非度规张量的存在，扩展了文献中在Weyl-Cartan几何特定框架下的当前结果。 该量在伪正交群下对曲率张量的不可约表示的十一个基本部分中起作用，其中三个部分表现出与在Weyl-Cartan几何中获得的类型相似的代数类型，而其余的一个包含三十个独立分量，并产生一种新的代数分类。 后者是通过其主零方向及其对齐程度推导出来的，得到了十六种主要的代数类型，这些类型可以细分为许多子类型。 作为直接应用，我们确定了Metric-Affine Gravity中具有自旋、膨胀和剪切电荷的最广泛静态和球对称黑洞解族的代数类型。 显示英文摘要

摘要： We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the presence of the traceless nonmetricity tensor. This quantity switches on four of the eleven fundamental parts of the irreducible representation of the curvature tensor under the pseudo-orthogonal group, in such a way that three of them present similar algebraic types as the ones obtained in Weyl-Cartan geometry, whereas the remaining one includes thirty independent components and gives rise to a new algebraic classification. The latter is derived by means of its principal null directions and their levels of alignment, obtaining a total number of sixteen main algebraic types, which can be split into many subtypes. As an immediate application, we determine the algebraic types of the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity.