AI 中文总结
研究$f(\mathcal{R})$引力理论中霍金辐射对原初黑洞的影响，发现与广义相对论相比，原初黑洞蒸发缓慢，质量约$5 \times 10^{13}$g或更低的非旋转黑洞可能存活，重塑暗物质问题解决方案格局，推动对替代引力理论的研究。
AI 中文摘要
爱因斯坦的广义相对论（GR）在描述引力现象方面非常成功。然而，现代宇宙学和天体物理学中的一些开放性问题（如暴胀、暗能量）表明需要对该框架进行扩展或修改。修正引力（MGR）理论，包括标量张量模型和高维方法，试图解决这些差距并与现有实验测试保持一致。本文研究了$f(\mathcal{R})$引力理论中的霍金辐射，重点关注其对作为潜在暗物质（DM）候选者的原初黑洞（PBHs）的影响。分析表明，与GR预测相比，PBHs在MGR中蒸发缓慢。具体而言，质量约为$5 \times 10^{13}$g或更低的非旋转黑洞到当前时期可能存活，这取决于MGR参数——质量阈值比GR中至少小约十倍。这种延迟的蒸发时间线对PBHs作为DM成分的可行性施加了宽松的新约束，从而重塑了DM问题可能解决方案的格局。这促使进一步研究替代引力理论及其宇宙学后果。
英文摘要
Einstein's theory of general relativity (GR) has been remarkably successful in describing gravitational phenomena. However, several open questions in modern cosmology and astrophysics (e.g. inflation, dark energy) suggest the need for extensions or modifications to this framework. Modified gravity (MGR) theories, including scalar-tensor models and higher-dimensional approaches, attempt to address these gaps while maintaining consistency with established experimental tests. This work investigates Hawking radiation within an $f(\mathcal{R})$ gravity theory, with $\mathcal{R}$ being scalar curvature, focusing on its implications for primordial black holes (PBHs) as potential dark matter (DM) candidates. Our analysis reveals that PBHs evaporate slowly in MGR compared to GR predictions. Specifically, we find that non-rotating black holes with masses $\sim 5 \times 10^{13}$ g or lower would have survived by the present epoch, depending on the MGR parameter-a mass threshold approximately at least ten times smaller than in GR. This retarded evaporation timeline imposes relaxed new constraints on the viability of PBHs as DM constituents, thereby reshaping the landscape of possible solutions to the DM problem. This motivates further investigation into alternative gravitational theories and their cosmological consequences.
Comments8 pages including 11 figures(13 png files); comments welcome
