Title: Topology of restricted phase space thermodynamics in Kerr-Sen-Ads black holes Show Chinese title

Title: 受限相空间热力学在Kerr-Sen-AdS黑洞中的拓扑结构

Abstract: In this study, we investigate the thermodynamic topology of the Kerr-Sen-Ads black hole in restricted phase space. In the restricted phase space, a new parameter, central charge $C$, and its conjugate parameter $\mu$ are introduced, omitting the well-known $PdV$ term in the first law of black hole thermodynamics. We study the local and global topology of the black hole by considering the black hole solution as topological defects in the free energy landscape. We compute the winding number and the total topological number at the thermodynamic defects. For our analysis, we have considered five ensembles of Kerr-Sen-Ads black holes in restricted phase space: fixed $(Q, J, C)$, fixed $(\phi, J, C)$, fixed $(Q,\Omega, C)$, fixed $(Q, J, \mu)$, and fixed $(\phi,\Omega, C)$, where $Q$ is the electric charge, $J$ is the angular momentum, $C$ is the central charge, $\phi$ is the electric potential conjugate to charge, $\Omega$ is the angular frequency conjugate to $J$, and finally, $\mu$ is the chemical potential. In the fixed $(Q, J, C)$, fixed $(\phi, J, C)$, and fixed $(Q, J, \mu)$ ensembles, we find a topological charge of $+1$. In the fixed $(Q,\Omega, C)$ and fixed $(\phi, \Omega, C)$ ensembles, depending on the values of the thermodynamic parameters, we find topological charges of $-1$, $0$, and $+1$. Interestingly, in ensembles where we find the topological charge to be $0$, we observe both Hawking-Page and Davies type phase transitions. We show that both types of these phase transitions can be studied using a common vector field, and the topological charges associated with Davies type and Hawking-Page phase transitions are $-1$ and $+1$, respectively. Show Chinese abstract

Abstract: 在本研究中，我们研究了限制相空间中的Kerr-Sen-Ads黑洞的热力学拓扑结构。 在限制相空间中，引入了一个新参数，中心电荷$C$及其共轭参数$\mu$，省略了黑洞热力学第一定律中的著名$PdV$项。 我们通过将黑洞解视为自由能景观中的拓扑缺陷来研究黑洞的局部和全局拓扑结构。 我们计算了热力学缺陷处的绕数和总拓扑数。 在我们的分析中，我们考虑了五组限制相空间中的Kerr-Sen-AdS黑洞：固定$(Q, J, C)$，固定$(\phi, J, C)$，固定$(Q,\Omega, C)$，固定$(Q, J, \mu)$，以及固定$(\phi,\Omega, C)$，其中$Q$是电荷，$J$是角动量，$C$是中心电荷，$\phi$是与电荷共轭的电势，$\Omega$是与$J$共轭的角频率，最后，$\mu$是化学势。 在固定$(Q, J, C)$、固定$(\phi, J, C)$和固定$(Q, J, \mu)$的集合中，我们发现拓扑电荷为$+1$。 在固定$(Q,\Omega, C)$和固定$(\phi, \Omega, C)$的系综中，根据热力学参数的值，我们发现拓扑电荷为$-1$、$0$和$+1$。有趣的是，在我们发现拓扑电荷为$0$的系综中，我们观察到霍金-佩吉型和戴维斯型相变。 我们表明，这两种相变都可以使用一个共同的矢量场来研究，与Davies型和Hawking-Page相变相关的拓扑电荷分别为$-1$和$+1$。