基于普朗克尺度修正运动学的史瓦西黑洞稳定性的环绕数分析
A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
浏览论文内容
中文总结 AI 辅助
研究普朗克尺度效应能否稳定史瓦西黑洞，通过在普朗克尺度修正运动学下分析其热力学拓扑，利用立方熵修正及熵 - 几何对应强制物理约束，发现此类MDR不会产生稳定黑洞，不同主导阶修正的MDR情况待探索。
中文摘要 AI 辅助
确定普朗克尺度效应是否能使黑洞稳定，这涉及到黑洞蒸发和量子引力一致性的基本问题。在此，我们在普朗克尺度修正运动学下分析史瓦西黑洞的热力学拓扑，使用从具有主导修正\(\eta E^3/E_P\)的著名唯象MDR导出的立方熵修正。通过熵 - 几何对应强制物理约束（\(S'(r_h)>0\)，\(T>0\)），我们发现对于修正参数的两种符号，都有一个\(w = -1\)和\(W = -1\)的单一不稳定分支。由于负质量/温度，第二个暗示稳定性（\(w = +1\)）的根被排除，且位于微扰区域之外。因此，这类MDR不会产生稳定的史瓦西黑洞。然而，具有不同主导阶修正的MDR可能表现不同，使得寻找普朗克尺度稳定化仍是一个未解决的问题。
英文摘要
Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology of Schwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction \(ηE^3/E_P\). Enforcing physical constraints (\(S'(r_h) > 0\), \(T > 0\)) via the entropy-geometry correspondence, we find a single unstable branch with \(w = -1\) and \(W = -1\) for both signs of the correction parameter. A second root suggesting stability (\(w = +1\)) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.
