AI 中文总结
研究非对易时空中带电反德西特黑洞的热力学拓扑，采用非对易参数微扰展开结合数值分析，利用广义离壳自由能框架，揭示非对易效应影响，证明体态与边界拓扑对应，还研究了残余质量下限及相关热力学量变化。
AI 中文摘要
我们研究了由洛伦兹涂抹物质分布源产生的非对易时空中带电反德西特黑洞的热力学拓扑。由于临界热力学量的精确解析解不可得，我们采用非对易参数的微扰展开，并通过数值分析验证所得表达式。利用广义离壳自由能框架，我们探索了热力学相空间的拓扑结构并评估了表征相变的相应缠绕数。结果表明，与标准雷斯纳 - 诺德斯特罗姆反德西特黑洞相比，非对易效应给热力学行为带来了定性修改。此外，我们证明了体态和边界描述具有相同的全局热力学拓扑，为它们拓扑结构的对应提供了有力证据。我们还研究了黑洞热力学第二定律所隐含的残余质量下限，并观察到非对易修正改变了关键热力学量，尤其强调了熵和最终黑洞质量。
英文摘要
We investigate the thermodynamic topology of charged AdS black holes in a non-commutative spacetime sourced by Lorentzian-smeared matter distributions. Since exact analytical solutions for the critical thermodynamic quantities are not available, we employ a perturbative expansion in the non-commutative parameter and validate the resulting expressions through numerical analysis. Using the generalized off-shell free-energy framework, we explore the topological structure of the thermodynamic phase space and evaluate the corresponding winding number that characterizes the phase transitions. Our results reveal that non-commutative effects introduce qualitative modifications to the thermodynamic behavior compared with the standard Reissner-Nordström AdS black hole. Furthermore, we demonstrate that the bulk and boundary descriptions possess an identical global thermodynamic topology, providing strong evidence for the correspondence between their topological structures. We also investigate the lower bound on the remnant mass implied by the second law of black-hole thermodynamics and observe that non-commutative corrections modify key thermodynamic quantities, with particular emphasis on the entropy and the final black-hole mass.
Commentsv1: 34 pages, many figures
