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arXiv 2102.01556gr-qc
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$f(R,T)$修正引力理论中的Morris-Thorne虫洞

Morris-Thorne Wormholes in $f(R,T)$ modified theory of gravity

A Chanda, S Dey, B C Paul

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23 pages, 15 figures
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摘要：

我们研究静态可穿越虫洞得到的莫里斯和索恩在广义相对论（GR）的框架下修改后的引力理论。修正的引力作用量$f(R,T)$是里奇标量（$R$）和能量动量张量（$T$）的迹的函数。对于修正的引力$f(R,T)=R+αR^{2}+λT$，其中$α$和$λ$是常数，我们得到了相应形状函数的正常物质虫洞解（WH）。在WH的喉部和远离喉部处检查能量状况。引力作用量中的耦合参数$α$和$λ$对调节物质成分起着重要作用。对于一个给定的$λ$，WH的解决方案中发现，在存在的外来物质在喉$α<0$。结果表明，在不含奇异物质的修正引力中，当$α>0$时，存在WH.我们考虑两种不同的形函数来研究奇异物质或正常物质中WH的存在性。在$λ\neq - 8 π$提供的各向异性流体条件下，存在一类WH解.在具有各向异性源和$λ= - 8 π$的喉道两侧的平坦渐近区域中，根据不通过定理，不允许WH。作为引力作用量中的$λ\rightarrow 0$，所有的能量条件都满足，混合形函数表明正常物质存在WH。

英文摘要：

We study static traversable wormholes obtained by Morris and Thorne in general relativity (GR) in the framework of a modified theory of gravity. The modified gravitational action $f(R,T)$ is a function of the Ricci scalar ($R$) and of the trace of the energy momentum tensor ($T$). For a modified gravity $f(R,T)=R+αR^{2}+λT$, where $α$ and $λ$ are constants, we obtain wormhole solutions (WH) with normal matter for a relevant shape functions. The energy conditions are checked at the throat and away from the throat of the WH. The coupling parameters $α$ and $λ$ in the gravitational action play an important role to accommodate the matter composition. For a given $λ$, WH solutions are found in the presence of exotic matter at the throat for $α<0$. It is shown that WH exists in the modified gravity without exotic matter when $α>0$. We consider two different shape functions to investigate the existence of WH in the presence of exotic or normal matter. A class of WH solutions exist with anisotropic fluid provided $λ\neq - 8 π$. In flat asymptotic regions on both sides of the throat with anisotropic source and $λ= - 8 π$, it does not permit WH as per no go theorem. As $λ\rightarrow 0$ in the gravitational action, all the energy conditions are obeyed with the hybrid shape function indicating existence of WH with normal matter.

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