f(T,τ)引力中的可穿越虫洞：非奇异部分的完整分类
Traversable wormholes in $f(T,τ)$ gravity: a complete classification of the non-exotic sector
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中文总结 AI 辅助
该研究在f(T,τ)引力框架下，针对静态球对称可穿越虫洞推导场方程，通过分析能量条件等，证明物质-挠率耦合可支撑非奇异的可穿越虫洞，并给出相关几何的分类与约束条件。
中文摘要 AI 辅助
我们研究f(T,τ)引力中的静态球对称可穿越虫洞，其中挠率标量T与物质能量-动量张量的迹τ耦合。我们考虑线性模型f(T,τ)=T+βτ，采用各向异性流体和平均压强物质拉格朗日量ℒₘ=⟨p⟩=(pᵣ+2pₜ)/3。针对未预先固定红移或形状函数的Morris-Thorne几何推导场方程。对于常数红移函数，能量条件问题呈现简单形式：在β>8π且b(r)>0的分支，当且仅当rb(r)非递增时，整个时空的能量密度以及零能、弱能和强能条件均满足；该条件还隐含渐近平坦性、喉部外b(r)<r以及b'(r₀)≤-1。允许的几何可表示为b(r)=r₀²h(r)/r，其中h(r₀)=1且h(r)为正且非递增。对于代表性族b(r)=r₀(r₀/r)ⁿ，当n≥1时满足零能、弱能和强能条件，而主能量条件要求n≥3(β-2π)/(β-6π)。我们还将物理物质与有效源分离，表明迹耦合可使物理物质保持非奇异，尽管有效源违反零能条件。最后，我们研究带有非常数红移函数的边界情况b(r)=r₀²/r：递减的红移函数可改善喉部的切向零能条件，但该改善无法在整个渐近平坦外部区域维持。这些结果表明，物质-挠率耦合可支撑一大类可穿越虫洞，无需奇异物理物质。
英文摘要
We study static and spherically symmetric traversable wormholes in $f(T,τ)$ gravity, where the torsion scalar $T$ is coupled to the trace $τ$ of the matter energy--momentum tensor. We consider the linear model $f(T,τ)=T+βτ$ with an anisotropic fluid and the mean-pressure matter Lagrangian $\Lm=\Pmean=(p_r+2p_t)/3$. The field equations are obtained for the Morris--Thorne geometry without fixing the redshift or shape function at the outset. For a constant redshift function, the energy-condition problem takes a simple form. On the branch $β>8π$ and for $b(r)>0$, the energy density together with the null, weak, and strong energy conditions is satisfied throughout the spacetime if and only if $r b(r)$ is non-increasing. The same condition also implies asymptotic flatness, $b(r)<r$ outside the throat, and $b'(r_0)\leq -1$. The allowed geometries can therefore be written as $b(r)=r_0^2 h(r)/r$, where $h(r_0)=1$ and $h(r)$ is positive and non-increasing. For the representative family $b(r)=r_0(r_0/r)^n$, the null, weak, and strong energy conditions hold for $n\geq1$, while the dominant energy condition requires $n\geq3(β-2π)/(β-6π)$. We also separate the physical matter from the effective source and show how the trace coupling allows the physical matter to remain non-exotic although the effective source violates the null energy condition. Finally, we examine the marginal case $b(r)=r_0^2/r$ with a non-constant redshift function. A decreasing redshift function can improve the tangential null energy condition at the throat, but this improvement cannot be maintained throughout an asymptotically flat exterior. These results show that the matter--torsion coupling can support a broad class of traversable wormholes without requiring exotic physical matter.
