In this work we analyze, in the context of modified teleparallel gravity, the equivalence between scalar-vector-tensor theories and geometrical theories of the type fT,B,∇μT,∇μB , where T and B are respectively the scalar torsion and the boundary scalar. This analysis is performed in the Jordan and Einstein frames. In particular, in the latter frame, two distinct cases are analyzed, where the role of surface terms is discussed. The equivalence between the geometrical and the scalar-vector-tensor approaches is verified for regular systems, i.e. for systems that present a regular Hessian matrix. An example is presented and the analysis of the Cauchy problem is made for the different approaches. An extension for systems that include higher-order derivatives of T and B is briefly presented, showing the equivalence between the geometrical and scalar-multi tensor theories.

中文翻译：

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fT,B,∇μT,∇μB 远平行引力的标量多张量方法

在这项工作中，我们在修正的远平行引力的背景下分析了标量矢量张量理论和该类型的几何理论之间的等价性 F时间,乙,∇μ时间,∇μ乙 ， 在哪里时间和乙分别是标量挠率和边界标量。该分析是在乔丹坐标系和爱因斯坦坐标系中进行的。特别是，在后一个框架中，分析了两种不同的情况，其中讨论了表面项的作用。对于正则系统，即对于呈现正则 Hessian 矩阵的系统，验证了几何方法和标量-矢量-张量方法之间的等价性。给出了一个例子，并对不同方法的柯西问题进行了分析。包含高阶导数的系统的扩展时间和乙简要介绍了几何张量理论和标量多张量理论之间的等价性。