发表机构
University of Burdwan（布尔达万大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Sultana-Dyer黑洞时空中研究Yamabe型孤子，证明非Killing向量场诱导$h$-几乎Yamabe孤子，并揭示其能量-动量张量与多种曲率结构的相容性及晚期膨胀下能量条件的违反。
AI 中文摘要
本文研究了Sultana-Dyer（SD）黑洞时空上的Yamabe型孤子结构。通过利用与SD时空相关的显式度量和曲率量，我们证明了非Killing向量场$\partial_t$在显式确定的函数$h$和$\lambda$下诱导出一个$h$-几乎Yamabe孤子。我们还建立了该结构退化为几乎Yamabe孤子的条件，并考察了为什么坐标向量场$\partial_r$和$\partial_\theta$不满足相应的Yamabe流条件。此外，我们证明了由类时尘埃分量和零辐射流体组成的能量-动量张量与黎曼、共形（Weyl）、共圆、共调和及射影曲率结构相容。这种相容性揭示了物质分布与时空因果结构之间的强几何对应关系。然而，当依赖于时间的标量曲率轮廓受到与晚期宇宙膨胀相关的约束时，零、弱和主能量条件被违反。这些发现为广义Yamabe孤子框架内的时间依赖Sultana-Dyer时空提供了几何刻画。
英文摘要
This paper investigates Yamabe-type soliton structures on the Sultana-Dyer (SD) black-hole spacetime. By employing the explicit metric and curvature quantities associated with the SD spacetime, we demonstrate that the non-Killing vector field $\partial_t$ induces an $h$-almost Yamabe soliton for explicitly determined functions $h$ and $λ$. We also establish the condition under which this structure reduces to an almost Yamabe soliton and examine why the coordinate vector fields $\partial_r$ and $\partial_θ$ do not satisfy the corresponding Yamabe flow conditions. Furthermore, we show that the energy-momentum tensor, consisting of a timelike dust component and a null radiation fluid, is compatible with the Riemann, conformal (Weyl), concircular, conharmonic, and projective curvature structures. This compatibility reveals a strong geometric correspondence between the matter distribution and the causal structure of the spacetime. However, when the time-dependent scalar-curvature profile is subject to the constraints associated with late-stage cosmic expansion, the null, weak, and dominant energy conditions are violated. These findings provide a geometric characterization of the time-dependent Sultana-Dyer spacetime within the framework of generalized Yamabe solitons.
Comments17 pages
