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arXiv 2006.07406gr-qc
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一类射影不变度量仿射引力理论中的各向异性形变

Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity

Jose Beltrán Jiménez, Daniel de Andrés, Adrià Delhom

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31 pages, 5 figures, 1 column
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摘要：

在一般的度量-仿射引力理论中，有一个特殊的类是由那些被赋予投射对称性的理论所确定的。也许实现这种对称性的最简单方式是根据里奇张量的对称部分构造作用量。在这些理论中，这种联系可以用与时空度规相关的度规，通过物质场给出的所谓变形矩阵，用代数方法解决。在大多数唯象学应用中，这个变形矩阵被假设继承了物质扇区的对称性，因此在各向同性能量-动量张量存在的情况下，它尊重各向同性。在这项工作中，我们讨论了这个条件，特别是，我们展示了如何变形矩阵可以是各向异性的，即使在各向同性源的存在下，由于非线性性质的方程。值得注意的是，我们发现，爱丁顿启发Born-Infeld理论不承认各向异性变形，但更一般的理论。然而，我们发现，各向异性分支的解决方案通常倾向于一种病态的物理行为。

英文摘要：

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.

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