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Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
Classical and Quantum Gravity ( IF 3.5 ) Pub Date : 2021-09-09 , DOI: 10.1088/1361-6382/ac2136
Alexey Golovnev

The f(T) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of tetrads. By using an appropriate spin connection it can be brought to a formally Lorentz invariant shape. However, despite some mathematical elegance obtained and new options of looking for non-standard couplings to matter probably made possible, it is fully equivalent in itself to the initial formulation. It seems that this fact, that the covariantisation does not in principle change anything, is not understood well by the community. Therefore we give a pedagogical introduction to these topics. And, on top of that, we show that obtaining the explicit equations for spherically symmetric solutions in f(T) gravity is not very difficult computationally and can be easily done even without any computer at hand.



中文翻译:

f(T) 引力中的洛伦兹不变性问题和球对称解的计算

所述˚FŤ) 引力现在被广泛用于宇宙学模型的构建,以及构建球对称解。在其经典的纯四分体公式中,它违反了四分体空间中的局部洛伦兹对称性。通过使用适当的自旋连接,它可以被带到形式上的洛伦兹不变形状。然而,尽管获得了一些数学上的优雅,并且可能使寻找非标准耦合的新选项成为可能,但它本身完全等同于初始公式。似乎这个事实,即协变原则上不会改变任何东西,社区并没有很好地理解。因此,我们对这些主题进行了教学介绍。并且,最重要的是,我们表明获得球对称解的显式方程f ( T ) 引力在计算上不是很困难,即使手头没有任何计算机也可以轻松完成。

更新日期:2021-09-09
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