Pub Date : 2025-12-05DOI: 10.1140/epjc/s10052-025-15133-6
Hao Chen, Meng-Yao Zhang, Hassan Hassanabadi, Qihong Huang, Zheng-Wen Long
This work explores the universal classification of thermodynamic topology for charged static black holes within the (z=3) Hor̆ava-Lifshitz gravity theory, considering both canonical and grand canonical ensembles. We introduce a new topological subclass, denoted as (ddot{W}^{1-}). This finding expands the existing topological classification, going beyond the five previously defined classes and their respective subclasses. The (ddot{W}^{1-}) subclass presents a distinct and previously unobserved stability profile: In the low-temperature regime, an unstable small black hole appears in the phase space, whereas, while in the high temperature regime, two unstable small black holes exist together with a stable large black hole. Our study underscores the dependence of charged black hole stability on the selection of the ensemble. These results contribute to refining and expanding the topological framework in black hole thermodynamics, providing key perspectives on the underlying nature of black holes and gravity.
这项工作探讨了在(z=3) Hor ā wa - lifshitz引力理论中带电静态黑洞热力学拓扑的普遍分类,同时考虑了正则和大正则系综。我们引入一个新的拓扑子类,表示为(ddot{W}^{1-})。这一发现扩展了现有的拓扑分类,超出了先前定义的五个类及其各自的子类。(ddot{W}^{1-})亚类呈现出一种独特的、以前未被观察到的稳定性剖面:在低温状态下,相空间中出现一个不稳定的小黑洞,而在高温状态下,两个不稳定的小黑洞与一个稳定的大黑洞一起存在。我们的研究强调了带电黑洞稳定性对系综选择的依赖性。这些结果有助于完善和扩展黑洞热力学的拓扑框架,为黑洞和引力的潜在本质提供关键视角。
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In the present work, we perform a combined analysis of the cross sections for (e^+ e^- rightarrow K^+ K^-) and (e^+ e^- rightarrow K_S^0 K_L^0) by including the interference between direct coupling process and resonance intermediate process. When setting the isospin factor as a free parameter, we can well reproduce the structures in the cross sections for (e^+ e^- rightarrow K^+ K^-) and (e^+ e^- rightarrow K_S^0 K_L^0,) however, the isospin factor deviates with the isospin symmetry conservation predicted value of one. By fixing the isospin factor to be one, we find the cross sections for (e^+ e^-rightarrow K^+ K^-) can be accurately fitted, while the same model parameters fail to adequately reproduce the observed cross section for the process (e^+ e^- rightarrow K_S^0 K_L^0,) which indicate that there should be contributions from other vector meson states, such as (rho (2150)) and (omega (2220).) The combined analysis with (phi (2170),)(omega (2220)) and (rho (2150)) indicate that the inclusion of (rho (2150)) can improve the descriptions of the cross sections for (e^+ e^-rightarrow K^+ K^-) and (e^+ e^- rightarrow K_S^0 K_L^0.)