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arXiv 2103.11698gr-qc
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理想流体$f\left(R,T\right)$引力中的结点条件和薄壳

Junction conditions and thin-shells in perfect-fluid $f\left(R,T\right)$ gravity

João Luís Rosa

摘要:

在这项工作中,我们得到的交界处的两个时空之间的匹配在分离超曲面的完美流体版本的$f\left(R,T\right)$引力,不仅在通常的几何表示,而且在一个动态等效的标量张量表示。我们从薄壳在分离超曲面处将两个时空分离的一般情况开始,推导出一般的接合条件,并考虑薄壳的应力-能量张量消失时光滑匹配的特殊情况。一组结的条件是类似的一个先前获得的$f\left(R\right)$重力,但功能也限制在应力能量张量$T_{ab}$及其偏导数,这迫使薄壳满足辐射状态方程$σ=2p_t$的轨迹。因此,球对称薄壳满足所有能量条件的充分必要条件是其能量密度$σ$为正。对于函数$f\left(R,T\right)$的特定形式,$R$和$T$的连续性不再是强制性的,但在分离超曲面处出现了引力双层。Martinez薄壳系统和围绕中心黑洞的薄壳作为应用的例子。

英文摘要:

In this work we derive the junction conditions for the matching between two spacetimes at a separation hypersurface in the perfect-fluid version of $f\left(R,T\right)$ gravity, not only in the usual geometrical representation but also in a dynamically equivalent scalar-tensor representation. We start with the general case in which a thin-shell separates the two spacetimes at the separation hypersurface, for which the general junction conditions are deduced, and the particular case for smooth matching is considered when the stress-energy tensor of the thin-shell vanishes. The set of junction conditions is similar to the one previously obtained for $f\left(R\right)$ gravity but features also constraints in the continuity of the trace of the stress-energy tensor $T_{ab}$ and its partial derivatives, which force the thin-shell to satisfy the equation of state of radiation $σ=2p_t$. As a consequence, a necessary and sufficient condition for spherically symmetric thin-shells to satisfy all the energy conditions is the positivity of its energy density $σ$. For specific forms of the function $f\left(R,T\right)$, the continuity of $R$ and $T$ ceases to be mandatory but a gravitational double-layer arises at the separation hypersurface. The Martinez thin-shell system and a thin-shell surrounding a central black-hole are provided as examples of application.

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