AI 中文总结
本研究探讨高维时空中经圈量子引力修正的黑洞，分析其引力坍缩过程、残余物特性、类弱引力猜想行为及邦迪吸积的爱丁顿光度，验证了相关不变量关系。
AI 中文摘要
我们研究高维时空中均匀尘埃球的引力坍缩，其通过修正的弗里德曼方程引入圈量子引力修正。该模型最显著的特征是形成一个终点：在有限的视界半径处温度消失，蒸发停止，留下一个残余物。将\\\\\\(\alpha\\\\
英文摘要
We study the gravitational collapse of a homogeneous dust sphere in higher-dimensional spacetime, with the loop quantum gravity correction entered through a modified Friedmann equation. Its most striking feature is an endpoint: at a finite horizon radius the temperature vanishes and evaporation stops, leaving a remnant. Reading \(α\) as an effective charge, we find behavior reminiscent of the Weak Gravity Conjecture (WGC), although no \(U(1)\) gauge field is present in the model. Solving the degeneracy conditions with the untruncated metric function, rather than with a mass expansion that is not uniform near the endpoint, we obtain closed-form expressions for the remnant radius and mass in \(D=4,5,6,7\). The unscaled ratio \(α/M_{\text{remnant}}^2\) is constant only in four dimensions and grows as \(α^{4-D}\) elsewhere, but it carries dimension \(L^{8-2D}\), so that growth is an artifact of the units. The dimensionless combination \(\tilde{\mathcal{R}} = (α/M^2) r_0^{2D-8}\) settles instead on a finite \(α\)-independent number in every dimension, decreasing from \(27/64\) in four dimensions to \(13824/(15625π^4)\) in seven. We also deform the quantum parameter, \(α\to α+ \varepsilon\), and evaluate \(-T(\partial S/\partial \varepsilon)_M\) in the remnant limit. Because \((\partial M/\partial r)_α\) vanishes there, the fixed-entropy derivative reduces exactly to a fixed-radius one, and the resulting combination \(\mathcal{U}\) is finite in each dimension but depends on \(\varepsilon\) except for \(D=5\). What is invariant is the product \(\mathcal{R}\,\mathcal{U}\,M_{\text{remnant}} = (D-3)/2\), which we verify numerically. Lastly, we study Bondi accretion onto the quantum-corrected black hole and obtain the Eddington luminosity for each dimension.
Comments23 pages, 14 figures, 5 table
