论文标题
一类投射不变的度量型重力理论的各向异性变形
Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity
论文作者
论文摘要
在公制的重力理论的一般类别中，有一个特殊的阶级，这些阶级由具有投射对称性的人构成。意识到这种对称性的最简单方式也许是根据Ricci张量的对称部分构建动作。在这些理论中，可以通过与时空指标相关的指标来通过所谓的变形矩阵来求解该连接。在大多数现象学应用中，假定该变形矩阵遗传物质扇区的对称性，因此在存在各向同性能量巨型张量的情况下，它尊重各向同性。在这项工作中，我们讨论了这种情况，尤其是我们展示了由于方程的非线性性质，即使在存在各向同性源的存在下，变形矩阵也可以是各向异性的。值得注意的是，我们发现，爱丁顿启发的侵袭性理论不承认各向异性变形，而是更一般的理论。但是，我们发现解决方案的各向异性分支通常容易出现病理的身体行为。
Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter sector so that in the presence of an isotropic energy-momentum tensor, it respects isotropy. In this work we discuss this condition and, in particular, we show how the deformation matrix can be anisotropic even in the presence of isotropic sources due to the non-linear nature of the equations. Remarkably, we find that Eddington-inspired-Born-Infeld theories do not admit anisotropic deformations, but more general theories do. However, we find that the anisotropic branches of solutions are generally prone to a pathological physical behaviour.
