理想流体$f(\mathcal{G},~T)$引力理论中的结条件
Junction conditions in perfect fluid $f(\mathcal{G},~T)$ gravitational theory
摘要：
本文旨在建立$f(\mathcal{G},~T)$引力的引力结条件。在这个引力理论中，$f$是高斯-博内不变量$\mathcal{G}$和能量-动量张量$T_{μν}$的迹的任意函数，即，$T$。我们首先介绍了这种引力理论在其通常的几何表示和postorly获得一个动态等效的标量张量演示上的任意依赖于通用函数$f$在$\mathcal G$和$T$是由两个标量场和标量位交换。然后，我们推导出两个不同的时空之间的匹配跨越分离超曲面$Σ$的JC，假设的物质部门所描述的各向同性的完美的流体配置。我们采用一般的方法，假设在两个时空之间的$Σ$处可能出现薄壳层。然而，我们的研究结果表明，分布形式主义是定义良好的，薄壳不允许出现在这个理论的一般版本。因此，我们得到一个完整的集，而不是在$Σ$在相同的条件下进行平滑匹配的JC。然后在理论的标量-张量表示中得到相同的结果，从而强调了这两种表示之间的等价性。我们的研究结果显着限制的可能性，替代紧凑的结构支持薄壳在$f(\mathcal{G},~T)$重力，例如重力星和薄壳虫洞的模型，但提供了一个合适的框架，搜索模型呈现出一个光滑的匹配在其表面，从完美的流体星是可能的例子。
英文摘要：
This manuscript aims to establish the gravitational junction conditions(JCs) for the $f(\mathcal{G},~T)$ gravity. In this gravitational theory, $f$ is an arbitrary function of Gauss-Bonnet invariant $\mathcal{G}$ and the trace of the energy-momentum tensor $T_{μν}$ i.e., $T$. We start by introducing this gravity theory in its usual geometrical representation and posteriorly obtain a dynamically equivalent scalar-tensor demonstration on which the arbitrary dependence on the generic function $f$ in both $\mathcal G$ and $T$ is exchanged by two scalar fields and scalar potential. We then derive the JCs for matching between two different space-times across a separation hyper-surface $Σ$, assuming the matter sector to be described by an isotropic perfect fluid configuration. We take the general approach assuming the possibility of a thin-shell arising at $Σ$ between the two space-times. However, our results establish that, for the distribution formalism to be well-defined, thin-shells are not allowed to emerge in the general version of this theory. We thus obtain instead a complete set of JCs for a smooth matching at $Σ$ under the same conditions. The same results are then obtained in the scalar-tensor representation of the theory, thus emphasizing the equivalence between these two representations. Our results significantly constrain the possibility of developing models for alternative compact structures supported by thin-shells in $f(\mathcal{G},~T)$ gravity, e.g. gravastars and thin-shell wormholes, but provide a suitable framework for the search of models presenting a smooth matching at their surface, from which perfect fluid stars are possible examples.
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